diff --git a/datasette/views/base.py b/datasette/views/base.py
index 14179824..7772f42d 100644
--- a/datasette/views/base.py
+++ b/datasette/views/base.py
@@ -228,6 +228,8 @@ class BaseView(RenderMixin):
 
         content_type = "text/plain; charset=utf-8"
         headers = {}
+        if self.ds.cors:
+            headers["Access-Control-Allow-Origin"] = "*"
         if request.args.get("_dl", None):
             content_type = "text/csv; charset=utf-8"
             disposition = 'attachment; filename="{}.csv"'.format(
diff --git a/tests/fixtures.py b/tests/fixtures.py
index 004a0b03..cc1734f4 100644
--- a/tests/fixtures.py
+++ b/tests/fixtures.py
@@ -23,32 +23,39 @@ class TestClient:
         )
 
 
-@pytest.fixture(scope='session')
-def app_client(sql_time_limit_ms=None, max_returned_rows=None, config=None, filename="fixtures.db"):
+@pytest.fixture(scope="session")
+def app_client(
+    sql_time_limit_ms=None,
+    max_returned_rows=None,
+    cors=False,
+    config=None,
+    filename="fixtures.db",
+):
     with tempfile.TemporaryDirectory() as tmpdir:
         filepath = os.path.join(tmpdir, filename)
         conn = sqlite3.connect(filepath)
         conn.executescript(TABLES)
         os.chdir(os.path.dirname(filepath))
-        plugins_dir = os.path.join(tmpdir, 'plugins')
+        plugins_dir = os.path.join(tmpdir, "plugins")
         os.mkdir(plugins_dir)
-        open(os.path.join(plugins_dir, 'my_plugin.py'), 'w').write(PLUGIN1)
-        open(os.path.join(plugins_dir, 'my_plugin_2.py'), 'w').write(PLUGIN2)
+        open(os.path.join(plugins_dir, "my_plugin.py"), "w").write(PLUGIN1)
+        open(os.path.join(plugins_dir, "my_plugin_2.py"), "w").write(PLUGIN2)
         config = config or {}
-        config.update({
-            'default_page_size': 50,
-            'max_returned_rows': max_returned_rows or 100,
-            'sql_time_limit_ms': sql_time_limit_ms or 200,
-        })
+        config.update(
+            {
+                "default_page_size": 50,
+                "max_returned_rows": max_returned_rows or 100,
+                "sql_time_limit_ms": sql_time_limit_ms or 200,
+            }
+        )
         ds = Datasette(
             [filepath],
+            cors=cors,
             metadata=METADATA,
             plugins_dir=plugins_dir,
             config=config,
         )
-        ds.sqlite_functions.append(
-            ('sleep', 1, lambda n: time.sleep(float(n))),
-        )
+        ds.sqlite_functions.append(("sleep", 1, lambda n: time.sleep(float(n))))
         client = TestClient(ds.app().test_client)
         client.ds = ds
         yield client
@@ -83,6 +90,11 @@ def app_client_with_dot():
     yield from app_client(filename="fixtures.dot.db")
 
 
+@pytest.fixture(scope='session')
+def app_client_with_cors():
+    yield from app_client(cors=True)
+
+
 def generate_compound_rows(num):
     for a, b, c in itertools.islice(
         itertools.product(string.ascii_lowercase, repeat=3), num
diff --git a/tests/test_csv.py b/tests/test_csv.py
index 194de5b1..398dbd1f 100644
--- a/tests/test_csv.py
+++ b/tests/test_csv.py
@@ -1,4 +1,8 @@
-from .fixtures import app_client, app_client_csv_max_mb_one # noqa
+from .fixtures import ( # noqa
+    app_client,
+    app_client_csv_max_mb_one,
+    app_client_with_cors
+)
 
 EXPECTED_TABLE_CSV = '''id,content
 1,hello
@@ -30,13 +34,21 @@ pk,planet_int,on_earth,state,city_id,city_id_label,neighborhood
 15,2,0,MC,4,Memnonia,Arcadia Planitia
 '''.lstrip().replace('\n', '\r\n')
 
+
 def test_table_csv(app_client):
     response = app_client.get('/fixtures/simple_primary_key.csv')
     assert response.status == 200
+    assert not response.headers.get("Access-Control-Allow-Origin")
     assert 'text/plain; charset=utf-8' == response.headers['Content-Type']
     assert EXPECTED_TABLE_CSV == response.text
 
 
+def test_table_csv_cors_headers(app_client_with_cors):
+    response = app_client_with_cors.get('/fixtures/simple_primary_key.csv')
+    assert response.status == 200
+    assert "*" == response.headers["Access-Control-Allow-Origin"]
+
+
 def test_table_csv_with_labels(app_client):
     response = app_client.get('/fixtures/facetable.csv?_labels=1')
     assert response.status == 200