That break-in was carried out in the town's James Dickson Place, off Farrier Court and Washington Avenue, at around 3.30am.
The man responsible, accompanied by a black Staffordshire bull terrier, fled after being disturbed.
He is described as white, 5ft 11in tall and of medium build. He was wearing a dark hooded top under a black puffer-style jacket and dark trousers.
Potential witnesses are asked to call Kelso police station on 101, quoting incident number 387 of April 3, or Crimestoppers anonymously on 0800 555111.