The man, described as in his early 20s, targeted the Lime Blue diamond store on George Street yesterday lunchtime.
He asked to see some rings and when the assistant removed a tray from the display cases and placed them on the counter, he grabbed them and ran out of the store, pursued by a member of staff.
He turned left and ran down Castle Street towards Queen Street where he got into a dark green car. Police are checking CCTV in a bid to trace it.
One eyewitness, who asked not to be named, said: “A lassie ran out after the robber.
“He ran straight out and struggled to get into a car that was waiting for him. The car bumped up on the pavement and eventually the guy got in.
“The car sped along the footpath for a bit, too, then just disappeared.”
Staff at the store refused to comment yesterday.
The thief is described as a thin, white male with short, dark, spiky hair. He was 5ft 6in tall and was wearing a dark blue jacket, jeans and white trainers.
Detective Sergeant Lynsey Thomson from Lothian and Borders Police said: “This was a brazen theft that happened on a busy street in broad daylight and we are confident that someone would have seen a male running down Castle Street.
“Similarly, anyone who may recognise a description of the suspect or the car should come forward immediately.”