Griffin made his league debut last season when he appeared for the last quarter of an hour in the home game against QPR but his only chance this season has been as an unused sub in the LDV Vans Trophy.
Griffin is still a trainee, and as such the Chester deal will be in the form of a work experience although it could run to the end of the season. Chester are currently third in the table and their joint-top scorer with 15 goals is another Athletic old-boy, Ryan Sugden.