UPDATE 3-Oil steadies above $110 on U.S. stocks, China data

* Best Chinese factory data for five months

* U.S. crude stocks fell by 7.2 million barrels last week

* Libya's western oilfields stay closed

* Coming up: U.S. weekly jobless claims; 1230 GMT

(Updates throughout, changes dateline, previous SINGAPORE)

LONDON, May 22 (Reuters) - Brent crude oil steadied near a 2-1/2-month high above $110 a barrel on Thursday, supported by better-than-expected data on China's manufacturing industry and a large draw in U.S. crude oil stocks.

China's factory sector turned in its best performance in five months in May, a preliminary HSBC survey showed, suggesting a brighter outlook for demand in the world's No.2 oil consumer.

"This is positive for oil markets, because better-than-expected factory orders will increase demand for oil. And coupled with commentary from the Fed overnight, oil prices will be supported for the time being," said Ben Le Brun, market analyst with OptionsXpress.

Brent crude was unchanged at $110.55 a barrel at 0730 GMT, just below a 2-1/2 month top of $110.73 reached on Wednesday. U.S. crude eased 5 cents to $104.02 a barrel. The U.S. contract settled up $1.74 on Wednesday, its biggest one-day gain in six weeks.

Commodities such as oil were supported by minutes of the U.S. Federal Reserve's last meeting that reassured investors that policy makers would continue to support the U.S. economy.

Oil prices also drew support from data showing a plunge in U.S. crude stocks last week as imports slumped to their lowest since 1997 as domestic production rose.

Crude inventories in the world's biggest oil consumer fell 7.2 million barrels last week, the Energy Information Administration (EIA) said, compared with analysts' expectations for an increase of 750,000 barrels.

Crude stocks at the Cushing, Oklahoma, delivery hub fell 225,000 barrels, EIA said.

Conflict in Libya also underpinned oil prices.

Explosions and heavy fighting with anti-aircraft guns could be heard near two military camps in Libya's capital, Tripoli, on Wednesday, witnesses said, two days after gunmen had stormed parliament in the worst violence in months.

The country's major western oilfields remain closed 10 days after the government said protesters blocking pipeline flows had agreed to leave, while total oil output edged higher, the National Oil Corp said.

Only the small 30,000 barrels per day (bpd) Wafa oilfield was producing normally in the west, NOC said. Oil output in the OPEC-member was around 230,000 bpd, well below the country's 1.6 million bpd capacity.

(Additional reporting by Jacob Gronholt-Pedersen in Singapore; Editing by William Hardy)