The incident happened at 11:53pm on December 29 and the police have released a description to help their investigation.
A man is reported to have forced entry through the front doors before stealing items from the store.
The man was wearing skinny-fit navy blue tracksuit bottoms with orange stripes up the side, a dark-coloured hoodie, black trainers, and a face covering.
A Darlington Police spokesperson said: “Can you help our officers who are investigating a burglary which happened at Lidl, on Yarm Road, on December 29?
“At 11.53pm a man forced entry through the front doors before stealing items from within the store.
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“The man was wearing skinny fit navy blue tracksuit bottoms with orange stripes up the side, black trainers, a dark coloured hoodie, gloves, and a face covering.
“If you have any information that could assist, please contact us on 101, quoting crime reference number CRI00589571.
“Information can also be submitted online at www.durham.police.uk.”