Police responded to a dairy robbery on Colombo St at about 6.45pm on Monday. Four offenders fled in a stolen vehicle after taking cigarettes.
The fourth offender is still on the run.
The vehicle was spotted by police on North Parade, Richmond about 11.12pm but it failed to stop when signalled by police.
Police pursued the vehicle. The offenders stopped and were arrested about 14 minutes later.
Three youths, aged 15, 16, 17 will appear in Youth Court on Monday. They are facing charges of aggravated robbery and unlawfully taking a vehicle.
"Nobody was injured but the victim was understandably very shaken by the incident," a police spokeswoman said.
The hold-up comes after a spate of robberies in Christchurch involving teenagers.
The Star reported robberies are part of an initiation to be part of the group.
About 10 robberies have taken place in different suburbs since the beginning of August.
CCTV footage shows a number of similarities between the robberies, including using hammers as weapons, the offenders disguising their identity completely using clothing and stealing cash, cigarettes, alcohol and food.
Four others were charged on August 23 in relation to a robbery at Buns Bakery in Phillipstown.