Jan 24 (Reuters) -ICE cotton futures gained on Wednesday to hit their highest levels in more than three months, supported by a drawdown in unsold inventories and a weaker U.S. dollar.

* Cotton contracts for March CTc1 rose 0.79 cent, or 0.9%, to 85.39 cents per lb by 11:59 a.m. ET (1659 GMT) after climbing to as much as 85.47 cents a lb, their highest since Oct. 16.

* "The crop is being priced by the sellers as not much left and in a month or two, we might get into a market that's just going to reflect U.S. tightness of supply," said Jim Nunn, owner of Tennessee-based cotton brokerage Nunn Cotton.

* Earlier this month, the U.S. Department of Agriculture's (USDA) World Agricultural Supply and Demand Estimates report projected U.S. ending stocks in 2023/24 will be 200,000 bales lower at 2.9 million bales.

* "The crop in the mid-South is sold, it's probably 10-15% left in farmers' hands and then a certain percentage of what has been sold is still on call, but a good bit of the cotton that was on call was fixed on Friday's rally," Nunn said.

* Prices rallied 1.7% to a near three-month high on Friday in their best session since Dec. 7.

* The natural fibre also benefited as the dollar eased 0.5%, making U.S. cotton less expensive for overseas buyers, and also absorbed some of the upbeat sentiment on Wall Street. USD/ .N

* Traders looked ahead to the USDA's weekly export sales report due on Thursday. EXP/COT

* In the grains market, Chicago soybean futures fell for the first time in three sessions, pressured by expectations of record South American supplies, while wheat and corn rose. GRA/

Reporting by Deep Vakil in Bengaluru; Editing by Shweta Agarwal