diff --git a/apps/api/src/app.ts b/apps/api/src/app.ts
index dae1fb2..5a5137a 100644
--- a/apps/api/src/app.ts
+++ b/apps/api/src/app.ts
@@ -10,6 +10,7 @@ import type { Config } from './config.js';
 import type { AppEnv } from './context.js';
 import { demoLimits } from './demo/limits.js';
 import { Notifier } from './push.js';
+import { securityHeaders } from './security-headers.js';
 import { activityRoutes, personalBestRoutes } from './routes/activities.js';
 import { clubRoutes } from './clubs/routes.js';
 import { adminRoutes } from './routes/admin.js';
@@ -36,6 +37,8 @@ export function createApp({
   notifier?: Notifier;
 }) {
   const app = new Hono<AppEnv>();
+  const indexHtml = config.webDir ? readIndexHtml(config.webDir) : undefined;
+  app.use('*', securityHeaders(config, indexHtml));
 
   if (config.logRequests) app.use(logger());
 
@@ -69,7 +72,9 @@ export function createApp({
   app.route('/api/integrations', integrationRoutes);
   app.all('/api/*', (c) => c.json({ error: 'Not found' }, 404));
 
-  if (config.webDir) serveWeb(app, config.webDir);
+  if (config.webDir && indexHtml !== undefined) {
+    serveWeb(app, config.webDir, indexHtml);
+  }
 
   return app;
 }
@@ -94,13 +99,16 @@ function withClientIp(req: Request, c: Context | null) {
 }
 
 /** Serves the built PWA, falling back to index.html for client-side routes. */
-function serveWeb(app: Hono<AppEnv>, webDir: string) {
+function readIndexHtml(webDir: string) {
   const indexPath = join(webDir, 'index.html');
   if (!existsSync(indexPath)) {
     console.warn(`WEB_DIR is set but ${indexPath} does not exist`);
-    return;
+    return undefined;
   }
-  const indexHtml = readFileSync(indexPath, 'utf8');
+  return readFileSync(indexPath, 'utf8');
+}
+
+function serveWeb(app: Hono<AppEnv>, webDir: string, indexHtml: string) {
   app.use(
     '*',
     serveStatic({
diff --git a/apps/api/src/security-headers.spec.ts b/apps/api/src/security-headers.spec.ts
new file mode 100644
index 0000000..1ea8f40
--- /dev/null
+++ b/apps/api/src/security-headers.spec.ts
@@ -0,0 +1,54 @@
+import { createHash } from 'node:crypto';
+import { mkdtempSync, writeFileSync } from 'node:fs';
+import { tmpdir } from 'node:os';
+import { join } from 'node:path';
+import { describe, expect, it } from 'vitest';
+import { inlineScriptHashes } from './security-headers.js';
+import { setup } from './test-utils.js';
+
+const THEME = "document.documentElement.dataset.theme = 'dark';";
+const sha = (s: string) =>
+  `'sha256-${createHash('sha256').update(s).digest('base64')}'`;
+
+function webDir() {
+  const dir = mkdtempSync(join(tmpdir(), 'openrun-web-'));
+  writeFileSync(
+    join(dir, 'index.html'),
+    `<html><head><script>${THEME}</script>` +
+      '<script type="module" crossorigin src="/assets/index.js"></script>' +
+      '</head><body></body></html>',
+  );
+  return dir;
+}
+
+describe('security headers', () => {
+  it('allows only the page’s own inline script', () => {
+    const html = `<script>${THEME}</script><script src="/a.js"></script>`;
+    expect(inlineScriptHashes(html)).toEqual([sha(THEME)]);
+  });
+
+  it('sends a content security policy with every response', async () => {
+    const { app } = setup({ WEB_DIR: webDir() });
+    for (const path of ['/', '/api/health']) {
+      const res = await app.request(path);
+      const csp = res.headers.get('content-security-policy') ?? '';
+      expect(csp).toContain(`script-src 'self' ${sha(THEME)}`);
+      expect(csp).toContain("frame-ancestors 'none'");
+      expect(csp).toContain('https://tile.openstreetmap.org');
+      expect(res.headers.get('x-frame-options')).toBe('DENY');
+      expect(res.headers.get('referrer-policy')).toBe(
+        'strict-origin-when-cross-origin',
+      );
+      // Plain HTTP here, so no HSTS.
+      expect(res.headers.get('strict-transport-security')).toBeNull();
+    }
+  });
+
+  it('asks browsers to stay on HTTPS when served over it', async () => {
+    const { app } = setup({ ORIGIN: 'https://run.example.com' });
+    const res = await app.request('/api/health');
+    expect(res.headers.get('strict-transport-security')).toBe(
+      'max-age=31536000',
+    );
+  });
+});
diff --git a/apps/api/src/security-headers.ts b/apps/api/src/security-headers.ts
new file mode 100644
index 0000000..5196a7e
--- /dev/null
+++ b/apps/api/src/security-headers.ts
@@ -0,0 +1,51 @@
+import { createHash } from 'node:crypto';
+import { secureHeaders } from 'hono/secure-headers';
+import type { Config } from './config.js';
+
+/** Map tiles; see OSM_STYLE in apps/web/src/components/maplibre.ts. */
+const TILES = 'https://tile.openstreetmap.org';
+
+/**
+ * Headers that keep browsers from running anything openRun didn't send, from
+ * framing it on another site, and (on HTTPS) from ever using plain HTTP.
+ *
+ * `indexHtml` is the built web app's page: its inline script (the theme, set
+ * before the first paint) is allowed by hash, so no other inline script runs.
+ */
+export function securityHeaders(config: Config, indexHtml?: string) {
+  return secureHeaders({
+    contentSecurityPolicy: {
+      defaultSrc: ["'self'"],
+      scriptSrc: ["'self'", ...inlineScriptHashes(indexHtml ?? '')],
+      // react-easy-crop adds a <style> tag for the logo picker.
+      styleSrc: ["'self'", "'unsafe-inline'"],
+      // blob: is the logo picker's preview of the chosen file.
+      imgSrc: ["'self'", 'data:', 'blob:', TILES],
+      // MapLibre's worker fetches the tiles.
+      connectSrc: ["'self'", TILES],
+      workerSrc: ["'self'", 'blob:'],
+      objectSrc: ["'none'"],
+      baseUri: ["'self'"],
+      formAction: ["'self'"],
+      frameAncestors: ["'none'"],
+    },
+    xFrameOptions: 'DENY',
+    // OpenStreetMap's tile servers require a Referer, so send the origin
+    // (never the path) to other sites.
+    referrerPolicy: 'strict-origin-when-cross-origin',
+    strictTransportSecurity: config.origin.startsWith('https:')
+      ? 'max-age=31536000'
+      : false,
+  });
+}
+
+/** 'sha256-…' sources for each inline <script> in the page. */
+export function inlineScriptHashes(html: string) {
+  return [...html.matchAll(/<script(?![^>]*\bsrc=)[^>]*>([\s\S]*?)<\/script>/g)]
+    .map((m) => m[1])
+    .filter((body) => body.trim())
+    .map(
+      (body) =>
+        `'sha256-${createHash('sha256').update(body).digest('base64')}'`,
+    );
+}
diff --git a/apps/web/src/components/maplibre.ts b/apps/web/src/components/maplibre.ts
index 7b7e7e9..4e178f6 100644
--- a/apps/web/src/components/maplibre.ts
+++ b/apps/web/src/components/maplibre.ts
@@ -18,7 +18,10 @@ export { type GeoJSONSource, LngLatBounds, MapLibreMap, NavigationControl };
 
 export const BRAND = '#0d9488';
 
-/** OpenStreetMap raster tiles; no API key needed. */
+/**
+ * OpenStreetMap raster tiles; no API key needed. Another tile host also needs
+ * adding to the Content-Security-Policy in apps/api/src/security-headers.ts.
+ */
 export const OSM_STYLE: StyleSpecification = {
   version: 8,
   sources: {
diff --git a/apps/web/src/main.tsx b/apps/web/src/main.tsx
index e12a993..b4ecf6b 100644
--- a/apps/web/src/main.tsx
+++ b/apps/web/src/main.tsx
@@ -1,3 +1,4 @@
+import './zod-config';
 import { QueryClient, QueryClientProvider } from '@tanstack/react-query';
 import { StrictMode } from 'react';
 import * as ReactDOM from 'react-dom/client';
diff --git a/apps/web/src/zod-config.ts b/apps/web/src/zod-config.ts
new file mode 100644
index 0000000..b58070a
--- /dev/null
+++ b/apps/web/src/zod-config.ts
@@ -0,0 +1,7 @@
+import { z } from 'zod';
+
+// Zod's faster parsing compiles code with `new Function`, which the server's
+// Content-Security-Policy blocks, and its check for that is reported as a
+// violation on every page. Zod runs the check as each schema is created, so
+// main.tsx imports this before anything else.
+z.config({ jitless: true });