A 63-year-old man was robbed twice within minutes while waiting for a bus home.
Police said the man was outside Swindon bus station on Monday when a man grabbed his gold necklaces and ran off.
The victim was left holding the broken links but a woman then snatched them and also ran away.
Police said the two necklaces were worth about £500. One had a dog tag and diamond and the inscription "Tony" and the other had a gold pendant scroll.
The theft happened at about 1240 BST.
The first suspect was described as white, aged about 21, 5ft 10in to 6ft tall, of average build and with short fair hair.
The woman was described as white, aged 18 to 20, 5ft 8in to 5ft 10in tall, slim, and with fair shoulder length hair.
The spokesman said the pair had run off in the same direction.
Witnesses are asked to contact police.