Yes, you can plug an Xbox controller into a Chromebook. The controller should work automatically once it is plugged in.
There are a few reasons why an Xbox controller might not connect to a Chromebook. One possibility is that the controller is not compatible with Chromebooks. Another reason could be that the driver for the controller is not installed on the Chromebook. If neither of these reasons seem to be the problem, then it is possible that there is some sort of issue with the Bluetooth connection.
