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The chopper helped rescue a surfer who paddled into trouble off the coast of Scarborough Beach about 7.30pm on Monday.
The surfer had become stuck in the waves, but was uninjured, a police spokeswoman said.
The helicopter, taken from the fleet in Auckland, started to fly around Christchurch yesterday in a trial planned to go until March 20.
"It is clear that air support offers benefits to our frontline policing by providing aerial surveillance and monitoring from a safe distance and with a wider picture - enabling an efficient response and resolution," he said.
Bush said police wanted to investigate whether there was demand to expand the Eagle service beyond Christchurch.
The helicopter is a Bell 429. There will still be two helicopters in Auckland.
'Guardian in the sky'
Meanwhile, Canterbury District Commander Superintendent John Price welcomed the arrival of the helicopter as a "guardian in the sky", and noted it would be in the air for the anniversary of the mosque attacks.
"We want to know that we can go about, as a community, reuniting and remembering that tragedy and the loss of lives so as a community we can heal and we can do that in a safe way," he said.
He also hoped the helicopter would help to bring safe ends to fleeing driver incidents - of which there had been 600 in Canterbury in the past year.
"To me the cost of safety, the cost of human harm, doesn't have a dollar value. So if we can make a difference in that space - and I'm confident that we will - then it will be all worthwhile," he said.
Price said the technology was an enhancement to what the police already have on the ground in the district.
"From a long way away they can zoom in, they can capture things like registration plates, they can identify the driver. If we've got someone at night time they've got infrared capability so they can find people either that are lost or that we need to find," he said.
He said he was regularly hearing stories about the "really big difference" the Eagle made in Auckland.
"As our roads become more congested, as our bad guys become badder, as they're using more and more powerful tools, we need to keep pace," he said.