Chalmers, who left Melrose at the end of last season to join the Oxfordshire club, cited “personal reasons” for leaving.
A statement from the Chinnor board read: “Following the non-attendance of Craig at many of the pre-season training sessions a meeting was held with Craig at which he advised that due to personal matters and pressure of his other commitments he felt unable to carry out his obligations to the club.
“It is of some regret and disappointment that the Club has been let down at this late stage.”
Chinnor have appointed Matt Goode and Andrew Smith as joint head coaches.
It was reported that Chalmers informed Chinnor a 140-mile road trip from his home to training was proving impractical while he continues to be employed by a security firm in London with regular trips home to see his family.
Chalmers represented Scotland 60 times, scoring 166 points and made one appearance for the British and Irish Lions. As well as Melrose, he played club rugby for Worcester, Harlequins, and the Pertemps Bees.