The issue was also raised at a meeting of Hungerford Town Council.
The incident happened at the grave of David Halligan, who died aged 24 in a traffic accident in August 2010.
Mr Halligan, a former John O’Gaunt School pupil known to friends as Doggy, lived in Church Way, Hungerford, and worked for town master thatcher Bob Boulton.
Friends and family created an elaborate memorial in his memory at St Saviour’s churchyard.
But his father Paul revealed: “Someone has stolen a set of wind chimes that were placed there. “It’s very upsetting. It’s a pretty low thing for someone to stoop to, to steal from a grave.”
Mr Halligan said he had heard anecdotal evidence of other instances of theft from the churchyard.
The family had initially feared that the wind chimes may have contravened churchyard rules and been officially removed.
But town mayor Martin Crane told a meeting of the town council that this was not so, and that it was a matter of theft.
The incident has been reported to police.
Anyone with information should contact Thames Valley Police via the 101 number.
Alternatively the Crimestoppers charity can be contacted on 0800 555 111.