A Sainsbury's Local convenience store opened in Great Suffolk Street on Monday morning - less than 20 metres from a Tesco Express shop.
The new shop opened at 7am on Monday and the first customers soon found themselves contending with faulty tills and a fire alarm.
Sainsbury's says that the new store has created 19 jobs.
A Costa Coffee outlet will open next door to Sainsbury's Local in the coming days.
In recent weeks Tesco, which opened its Express store three years ago, has stepped up marketing activity for its Great Suffolk Street shop, handing out vouchers, Oyster card wallets and running a competition for tickets to Shakespeare's Globe and The Shard.
Sainsbury's is also distributing money-off coupons in the area.
Both convenience stores are open 7am-11pm seven days a week.