diff --git a/ops/storage.py b/ops/storage.py
index 5dda21d..9f259f4 100644
--- a/ops/storage.py
+++ b/ops/storage.py
@@ -18,6 +18,7 @@ import os
 import pickle
 import shutil
 import sqlite3
+import stat
 import subprocess
 from datetime import timedelta
 from pathlib import Path
@@ -59,11 +60,29 @@ class SQLiteStorage:
             # sqlite3.connect creates the file silently if it does not exist
             logger.debug(f"Initializing SQLite local storage: {filename}.")
 
+        if filename != ":memory:":
+            self._ensure_db_permissions(str(filename))
         self._db = sqlite3.connect(str(filename),
                                    isolation_level=None,
                                    timeout=self.DB_LOCK_TIMEOUT.total_seconds())
         self._setup()
 
+    def _ensure_db_permissions(self, filename: str):
+        """Make sure that the DB file has appropriately secure permissions."""
+        mode = stat.S_IRUSR | stat.S_IWUSR
+        if os.path.exists(filename):
+            try:
+                os.chmod(filename, mode)
+            except OSError as e:
+                raise RuntimeError(f"Unable to adjust access permission of {filename!r}") from e
+            return
+
+        try:
+            fd = os.open(filename, os.O_CREAT | os.O_EXCL, mode=mode)
+        except OSError as e:
+            raise RuntimeError(f"Unable to adjust access permission of {filename!r}") from e
+        os.close(fd)
+
     def _setup(self):
         """Make the database ready to be used as storage."""
         # Make sure that the database is locked until the connection is closed,

diff --git a/test/test_storage.py b/test/test_storage.py
index 2d58b75..b8467c8 100644
--- a/test/test_storage.py
+++ b/test/test_storage.py
@@ -17,10 +17,12 @@ import gc
 import io
 import os
 import pathlib
+import stat
 import sys
 import tempfile
 import typing
 import unittest
+import unittest.mock
 from test.test_helpers import BaseTestCase, fake_script, fake_script_calls
 from textwrap import dedent
 
@@ -218,6 +220,41 @@ class TestSQLiteStorage(StoragePermutations, BaseTestCase):
     def create_storage(self):
         return ops.storage.SQLiteStorage(':memory:')
 
+    def test_permissions_new(self):
+        with tempfile.TemporaryDirectory() as temp_dir:
+            filename = os.path.join(temp_dir, ".unit-state.db")
+            storage = ops.storage.SQLiteStorage(filename)
+            self.assertEqual(stat.S_IMODE(os.stat(filename).st_mode), stat.S_IRUSR | stat.S_IWUSR)
+            storage.close()
+
+    def test_permissions_existing(self):
+        with tempfile.TemporaryDirectory() as temp_dir:
+            filename = os.path.join(temp_dir, ".unit-state.db")
+            ops.storage.SQLiteStorage(filename).close()
+            # Set the file to access that will need fixing for user, group, and other.
+            os.chmod(filename, 0o744)
+            storage = ops.storage.SQLiteStorage(filename)
+            self.assertEqual(stat.S_IMODE(os.stat(filename).st_mode), stat.S_IRUSR | stat.S_IWUSR)
+            storage.close()
+
+    @unittest.mock.patch("os.path.exists")
+    def test_permissions_race(self, exists: unittest.mock.MagicMock):
+        exists.return_value = False
+        with tempfile.TemporaryDirectory() as temp_dir:
+            filename = os.path.join(temp_dir, ".unit-state.db")
+            # Create an existing file, but the mock will simulate a race condition saying that it
+            # does not exist.
+            open(filename, "w").close()
+            self.assertRaises(RuntimeError, ops.storage.SQLiteStorage, filename)
+
+    @unittest.mock.patch("os.chmod")
+    def test_permissions_failure(self, chmod: unittest.mock.MagicMock):
+        chmod.side_effect = OSError
+        with tempfile.TemporaryDirectory() as temp_dir:
+            filename = os.path.join(temp_dir, ".unit-state.db")
+            open(filename, "w").close()
+            self.assertRaises(RuntimeError, ops.storage.SQLiteStorage, filename)
+
 
 def setup_juju_backend(test_case: unittest.TestCase, state_file: pathlib.Path):
     """Create fake scripts for pretending to be state-set and state-get."""

.unit-state.db is world-readable
.unit-state.db created by an operator framework charm is visible by any user in the system. The permission should be tighten up.

This is one example of charms that saved a private key for a TLS certificate.
```
$ sudo -u nobody strings /var/lib/juju/agents/unit-ceph-dashboard-1/charm/.unit-state.db | grep PRIVATE
-----BEGIN RSA PRIVATE KEY-----
-----END RSA PRIVATE KEY-----
```
test/test_storage.py::TestSQLiteStorage::test_permissions_existing test/test_storage.py::TestSQLiteStorage::test_permissions_failure test/test_storage.py::TestSQLiteStorage::test_permissions_new test/test_storage.py::TestSQLiteStorage::test_permissions_race
test/test_storage.py::TestSQLiteStorage::test_all_notices test/test_storage.py::TestSQLiteStorage::test_drop_snapshot test/test_storage.py::TestSQLiteStorage::test_emit_event test/test_storage.py::TestSQLiteStorage::test_load_notices test/test_storage.py::TestSQLiteStorage::test_save_and_load_snapshot test/test_storage.py::TestSQLiteStorage::test_save_and_overwrite_snapshot test/test_storage.py::TestSQLiteStorage::test_save_load_drop_load_notices test/test_storage.py::TestSQLiteStorage::test_save_notice test/test_storage.py::TestSQLiteStorage::test_save_one_load_another_notice test/test_storage.py::TestSQLiteStorage::test_save_snapshot_empty_string test/test_storage.py::TestSQLiteStorage::test_save_snapshot_none test/test_storage.py::TestSQLiteStorage::test_save_snapshot_zero test/test_storage.py::TestJujuStorage::test_all_notices test/test_storage.py::TestJujuStorage::test_drop_snapshot test/test_storage.py::TestJujuStorage::test_emit_event test/test_storage.py::TestJujuStorage::test_load_notices test/test_storage.py::TestJujuStorage::test_save_and_load_snapshot test/test_storage.py::TestJujuStorage::test_save_and_overwrite_snapshot test/test_storage.py::TestJujuStorage::test_save_load_drop_load_notices test/test_storage.py::TestJujuStorage::test_save_notice test/test_storage.py::TestJujuStorage::test_save_one_load_another_notice test/test_storage.py::TestJujuStorage::test_save_snapshot_empty_string test/test_storage.py::TestJujuStorage::test_save_snapshot_none test/test_storage.py::TestJujuStorage::test_save_snapshot_zero test/test_storage.py::TestSimpleLoader::test_forbids_some_types test/test_storage.py::TestSimpleLoader::test_handles_tuples test/test_storage.py::TestSimpleLoader::test_is_c_dumper test/test_storage.py::TestSimpleLoader::test_is_c_loader test/test_storage.py::TestJujuStateBackend::test_get test/test_storage.py::TestJujuStateBackend::test_is_available test/test_storage.py::TestJujuStateBackend::test_is_not_available test/test_storage.py::TestJujuStateBackend::test_set_and_get_complex_value test/test_storage.py::TestJujuStateBackend::test_set_encodes_args