A Nabors rig reached a target surface section depth of 4,875 feet, Exxon said, adding it plans to complete the well to its full depth by the end of next year.
The company couldn't drill deeper this summer, as state regulations forbid penetrating hydrocarbon-bearing rock between April 15 and Nov. 1.
The well is part of the first phase of Exxon's planned $1.3 billion natural gas cycling project at Point Thomson. The remote field straddles the Beaufort Sea coastline about 60 miles east of Prudhoe Bay.
Exxon has said it aims to produce 10,000 barrels of gas condensate per day for shipment down the trans-Alaska oil pipeline.
Other major Point Thomson owners participating in the drilling include BP and Conoco Phillips.
"We are on schedule to begin production at Point Thomson by year-end 2014," said Dale Pittman, Exxon's Alaska production manager.
Point Thomson holds an estimated 8 trillion cubic feet of gas -- about a quarter of all the known gas reserves on the North Slope -- plus about 200 million barrels of condensate, Exxon said.
The gas is considered a crucial component for a proposed multibillion-dollar natural gas pipeline from the Slope into Canada.
This year's drilling activity is the first at Point Thomson since 1983.
Lack of production there long has been a sore point for the state, Exxon's landlord. In recent years, state officials have taken steps to prod the oil companies toward development, which means tax and royalty revenue plus jobs.
Those steps included terminating the Point Thomson unit and declaring that leases within the unit had expired.
For many years Exxon argued that production from Point Thomson was uneconomic or impractical for lack of a North Slope natural gas pipeline. Last year it offered up the gas cycling project as part of a strategy to keep the Point Thomson acreage, which state officials had declared they were prepared to offer for lease to new owners.
Last January, state Natural Resources Commissioner Tom Irwin reinstated two of the 31 leases. In exchange, Exxon would have to keep its pledge to start drilling there right away.
The larger fight for control of the Point Thomson is far from over.
Irwin has yet to issue his final decision on the status of Point Thomson leases.
Possibly more important is a forthcoming ruling from state Superior Court Judge Sharon Gleason. She is likely to decide by the end of the year whether the state was right -- or wrong, as Exxon and other companies argue -- in terminating the Point Thomson unit.
If the judge sides with Exxon, the effect is to extend leases that otherwise would have expired long ago.
However, the losing party is likely to appeal to the Alaska Supreme Court.
Important warning about e-mails purporting to be from the adn.com staff.