* Brent reaches $71.20, highest since December 2014
* OPEC-led oil supply curbs support market
* U.S. inventories fall for a record 10th straight week
* U.S. Treasury Secretary welcomes weaker U.S. dollar (Updates prices, adds context)
LONDON, Jan 25 (Reuters) - Oil hit $71 a barrel on Thursday for the first time since 2014, supported by OPEC-led supply curbs, a record-breaking run of declines in U.S. crude inventories and a weaker U.S. dollar.
The Organization of the Petroleum Exporting Countries and its allies including Russia began reining in supplies in January 2017. An involuntary drop in Venezuela's output in recent months has deepened the impact of those cuts.
Brent crude, the international oil benchmark, hit $71.20 a barrel, the highest since early December 2014. At 1320 GMT, Brent eased to $71.00 but still up 47 cents.
U.S. crude climbed to $66.44, also the highest since early December 2014, before dipping to $66.35, up 74 cents.
"The continuous fall in U.S. oil inventories and the prolonged weakness in the U.S. dollar have done the trick," said Tamas Varga of broker PVM, referring to oil hitting a new high.
Brent had traded above $110 a barrel in mid-2014 but in December 2014 it tumbled below $60 as the fall accelerated after OPEC's landmark decision in November of that year to end output restraint.
Prices had crashed to almost $27 by early 2016, prompting OPEC to change tack and forge a deal with Russia and others to curb output. Cuts began at the start of 2017 and will run to the end of 2018.
In a further sign the glut is clearing, U.S. crude inventories fell for a record 10th straight week to the lowest since February 2015, official figures showed on Wednesday.
Also supporting oil, the U.S. dollar hit its lowest since December 2014 against a basket of other currencies. U.S. Treasury Secretary Steven Mnuchin said on Wednesday a weaker dollar was "good for us".
A weaker dollar makes dollar-denominated commodities cheaper for holders of other currencies and tends to support oil prices.
"The depreciation of the U.S. dollar is also allowing oil prices to make further gains," said Carsten Fritsch, analyst at Commerzbank. "Almost every commodity class is being driven up by this extended dollar fall."
However, rising U.S. shale oil output has cast a shadow over the oil rally, as higher prices encourage more investment in expanding supplies.
U.S. crude oil production is expected to surpass 10 million barrels per day (bpd) in February, on the way to a record ahead of previous forecasts, according to the U.S. Energy Information Administration.
(Additional reporting by Henning Gloystein and Aaron Sheldrick; Editing by David Evans and Edmund Blair)