Whitelist experimental.storage as an unprivileged extension API.

chrome/common/extensions/api/extension_api.json

 [
   {
     "namespace": "extension",
     "types": [
       {
         "id": "MessageSender",
         "type": "object",
         "description": "An object containing information about the script context that sent a message or request.",
         "properties": {
           "tab": {"$ref": "Tab", "optional": true, "description":"This property will <b>only</b> be present when the connection was opened from a tab or content script."},
@@ skipping 1145 matching lines @@
             "type": "string",
             "description": "The namespace (\"sync\" or \"local\") of the storage area the changes are for."
           }
         ]
       }
     ],
     "properties": {
       "sync": {
         "$ref": "StorageNamespace",
         "description": "Items under the \"sync\" namespace are synced using Chrome Sync.",
+        "unprivileged": true,
         "value": [ "sync" ]
       },
       "local": {
         "$ref": "StorageNamespace",
         "description": "Items under the \"local\" namespace are local to each machine.",
+        "unprivileged": true,
         "value": [ "local" ]
       }
     }
   },
   {
     "namespace": "windows",
     "types": [
       {
         "id": "Window",
         "type": "object",
@@ skipping 8166 matching lines @@
                   }
                 }
               }
             ]
           }
         ]
       }
     ]
   }
 ]