Momoho-1 is expected to take about 40 days to drill to a total depth of about 3142m.
Minority Kupe partner New Zealand Oil & Gas had said previously it expects the Momoho prospect to contain estimated total recoverable reserves of about 200 billion cubic feet equivalent of gas in both gas and liquids.
Momoho sits between two exploration wells drilled about 20 years ago - Kupe South-4, a sub-commercial gas-condensate discovery, and Kupe South-5, which flowed sub-commercial quantities of oil and some gas.
Kupe project director Peter Ashford said that since the Kupe project was approved in June 2006, Origin had been looking for exploration opportunities close to production facilities.
Extensive geological and geophysical investigations had identified the Momoho prospect as the most exciting drilling candidate in the area, he said.
"If the results are encouraging, further appraisal may be required," Ashford added.
NZOG had said earlier there are several other mapped prospects, including Deby and Leith, adjacent to the Kupe central field area that could contain another 200Bcfe or so of reserves.
The potential to tie back future near-field discoveries has been incorporated into the Kupe development infrastructure.
The Kupe partners are operator Origin Energy (50%), Genesis Energy (31%), New Zealand Oil & Gas (15%), and Mitsui E&P NZ (4%).