Fiji Airways has round-trip flights from Dallas (DFW) to Christchurch (CHC) for $877 with a connection. Flights December, January, February, March, May, and June. Departures on Tuesday and Thursday. Extended weekends available. No Christmas dates available.
Some small OTAs on Skyscanner and Google have this for as low as $744; which is cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.