* Wheat gains for second session on global supply worries

* Drought-damaged oat crop supports corn

CHICAGO, Sept 23 (Reuters) - Chicago wheat futures firmed on Thursday, strengthened by global supply concerns and a firming oat futures market on drought-stricken North American supplies.

Corn and soybeans edged higher, supported by wheat and oats.

The most-active wheat contract on the Chicago Board Of Trade (CBOT) added 12 cents to $7.17-3/4 a bushel.

Soybeans gained 1-1/2 cents to $12.84-1/4 a bushel and corn added 3-3/4 cents at $5.29-1/4 a bushel.

Oats, primarily grown in Canada, North Dakota and Montana, suffered from severe drought that has decimated production.

"The crop was about halved," said Jeff French, owner of Ag Hedgers. "I think it’s going to go higher. Cash oats are leading the way."

The most-active oat futures added 21-1/2 cents to $5.79-1/4 a bushel, a 3.85% gain, the highest on record.

Corn futures firmed despite a quickly progressing harvest across much of the U.S. Midwest.

"Everything’s starting to dry down really fast now," said Mark Schultz, chief analyst at Northstar Commodity. "I wouldn’t be surprised if I had customers done with corn and beans by the 5th of October."

As farmers harvest, a previously tight corn and soybean supply is once again in focus, made clear by a firming cash basis across the U.S. Midwest, Schultz said.

"I just think we’re tight. I’ve never seen people bid for corn, both at ethanol plants and livestock feed mills, this deep into the year."

Meanwhile, U.S. export sales firmed as hurricane-damaged Gulf export terminals come online. Soybean export sales last week totaled 912,900 tonnes, near the high end of market forecasts that ranged from 500,000 to 1.1 million tonnes, according to the U.S. Department of Agriculture.

Export sales of 373,000 tonnes of corn were near the low end of trade expectations for 300,000 to 800,000 tonnes. (Reporting by Christopher Walljasper, additional reporting by Naveen Thukral; editing by Diane Craft)