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The man was captured on CCTV walking out of the Maclaggan St store on Thursday last week at 5.22pm, Sergeant Steve Aitken, of Dunedin, said.
He had somehow opened a locked cabinet, removing cellphones, PS3, PS4, and Nintendo 3DS XL, consoles, valued at $10,000.
He put the items into two plastic bags before making his way out of the store, Sgt Aitken said.
The incident was reported to police yesterday.
Anyone with information was urged to contact Dunedin Police on 471-4800, or anonymously via Crimestoppers on 0800 555 111.