diff --git a/fastapi/security/oauth2.py b/fastapi/security/oauth2.py
index 7ca7f6bc5..4f4bd3001 100644
--- a/fastapi/security/oauth2.py
+++ b/fastapi/security/oauth2.py
@@ -705,7 +705,7 @@ class OAuth2ClientCredentials(OAuth2):
                     headers={"WWW-Authenticate": "Bearer"},
                 )
             else:
-                return None  # pragma: nocover
+                return None
         return param
 
 
diff --git a/tests/test_security_oauth2_client_credentials_optional.py b/tests/test_security_oauth2_client_credentials_optional.py
new file mode 100644
index 000000000..f281a61a3
--- /dev/null
+++ b/tests/test_security_oauth2_client_credentials_optional.py
@@ -0,0 +1,72 @@
+from typing import Optional
+
+from fastapi import FastAPI, Security
+from fastapi.security import OAuth2ClientCredentials
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+
+oauth2_scheme = OAuth2ClientCredentials(tokenUrl="token", auto_error=False)
+
+
+@app.get("/items/")
+async def read_items(token: Optional[str] = Security(oauth2_scheme)):
+    return {"token": token}
+
+
+client = TestClient(app)
+
+
+def test_no_token():
+    response = client.get("/items")
+    assert response.status_code == 200, response.text
+    assert response.json() == {"token": None}
+
+
+def test_incorrect_token():
+    response = client.get("/items", headers={"Authorization": "Non-existent testtoken"})
+    assert response.status_code == 200, response.text
+    assert response.json() == {"token": None}
+
+
+def test_token():
+    response = client.get("/items", headers={"Authorization": "Bearer testtoken"})
+    assert response.status_code == 200, response.text
+    assert response.json() == {"token": "testtoken"}
+
+
+def test_openapi_schema():
+    response = client.get("/openapi.json")
+    assert response.status_code == 200, response.text
+    assert response.json() == {
+        "openapi": "3.1.0",
+        "info": {"title": "FastAPI", "version": "0.1.0"},
+        "paths": {
+            "/items/": {
+                "get": {
+                    "responses": {
+                        "200": {
+                            "description": "Successful Response",
+                            "content": {"application/json": {"schema": {}}},
+                        }
+                    },
+                    "summary": "Read Items",
+                    "operationId": "read_items_items__get",
+                    "security": [{"OAuth2ClientCredentials": []}],
+                }
+            }
+        },
+        "components": {
+            "securitySchemes": {
+                "OAuth2ClientCredentials": {
+                    "type": "oauth2",
+                    "flows": {
+                        "clientCredentials": {
+                            "tokenUrl": "token",
+                            "scopes": {},
+                        }
+                    },
+                }
+            }
+        },
+    }