Partner Karoon Gas said the well, Poseidon-1 in WA-315-P, was spudded on Monday and is currently drilling ahead at 1055m.
Poseidon-1 lies about 480 kilometres north of Broome and is targeting potential hydrocarbons in the middle and upper Jurassic sandstones.
The well is being drilled with the Sedco-703 rig and has a planned total depth of 4800m.
The Sedco-703 rig - which has been contracted for 200-225 days - is also expected to drill wells in WA-315-P and WA-398-P.
The JV's Browse Basin acreage is adjacent to the giant Torosa, Brecknock, and Caliance gas and condensate fields currently being appraised by a Woodside Petroleum JV.
The fields have a proven P50 resource of 21 trillion cubic feet of gas and 300 million barrels of condensate.
The Browse acreage is also near the Ichthys gas and condensate field, which is estimated to contain 12tcf of gas and 600MMbbl of condensate.
Karoon has said exploration success could lead to an Australian liquefied natural gas project that would be well placed to meet Asian demand for security, speed and reliability of supply.
ConocoPhillips is operator of the three permits and has a 51% interest in WA-314-P and WA-315-P, and a 60% interest in WA-398-P.
Karoon has a 49% interest in WA-314-P and WA-315-P, and a 40% interest in WA-398-P.