* Weekly U.S. export data delayed to Friday

* Worries that demand hurt by 8-pct price rise from Nov lows

* Spot cotton prices on track for 1st annual gain in 3 years

NEW YORK, Dec 26 (Reuters) - Cotton futures eased on Thursday in razor thin volumes, weighed by a lack of commercial buying during the holiday week and worries that high prices will further crimp demand.

The benchmark March cotton contract on ICE Futures U.S. closed down 0.29 cent, or 0.3 percent, at 82.89 cents a lb after trading in a tight range of about 1 cent throughout the day.

Fiber underperformed the broader commodities basket, with the majority of the 19 components of Thomson Reuters/Core Commodity CRB index gaining.

U.S. financial markets rose as jobless claims dropped more than expected, igniting hopes of a stronger labor market and supporting expectations of faster economic growth in 2014.

Trading volumes were extremely light after a delayed opening at 8 a.m. EST (1300 GMT), following the Christmas holiday on Wednesday.

Weekly U.S. government export data was delayed because of the holiday and due on Friday.

The March contract has recovered 8 percent from a trough of 76.65 cents a lb set a month ago, and worries have grown that the price recovery will continue to crimp demand.

Those worries kept a lid on Thursday's earlier gains and sent prices to a lower close.

"The export sales report is out tomorrow, and there are some expectations that we'll see lower demand," said Jack Scoville, a vice president for Price Futures Group in Chicago.

Imports in top consumer China have fallen 23 percent in the first 11 months of the year from the same period in 2012, official data showed this week.

Even so, a sense of tight U.S. supplies has underpinned futures prices.

That has pushed the market into a backwardation, with nearby prices trading at a premium, as farmers in the world's top grower finish harvesting their smallest crop in four years.

The spot contract has traded above second-month prices for the last 11 sessions.

Exchange inventories fell to 35,300 bales on Tuesday, down sharply from 225,600 at the start of the month, according to the most recent ICE data compiled by Reuters.

Even with the day's loss, spot cotton futures were on track to finish 2013 up 10 percent after posting big losses in 2011 and 2012.

(Reporting by Chris Prentice; Editing by Marguerita Choy)