MONEY MARKETS-Investors give U.S. a free 1-month loan

* U.S. 4-week bill auction has high rate of 0 percent

* T-bill rates fall for 2nd day in safety bid

* Two-year euro zone swap spread wider on Greek woes

* Euro Libor holds steady, likely to edge up into year-end

By Chris Reese

NEW YORK, Dec 8 (Reuters) - Investors gave the U.S. government a free one-month loan on Tuesday as they sought the safest possible haven to keep their cash through year end.

The high rate of zero percent in a Treasury auction of 4-week bills matches the lowest on record for the security and shows investors are keen to protect gains made this year, with banks especially eager to show top-quality assets on their balance sheets over the year end.

"This is the first bill that will get you over the end of the year and mature at the first week of the year so as a new issue, the ability to park cash, this was the first chance that you had to do that," said George Goncalves, head of fixed income rates strategy at Cantor Fitzgerald in New York, adding "it gives you a more pristine balance sheet."

One-month Treasury bill rates also eased for a second day on Tuesday as investors bought up safe-haven assets in worries over Greece's fiscal woes and expectations the U.S. Federal Reserve is nowhere near raising interest rates.

One-month Treasury bill US1MT=RR rates eased to 0.079 percent from 0.084 percent late on Monday and O.152 percent late on Friday.

Those rates climbed to the highest in nearly four months on Friday after a much-smaller-than-expected contraction in U.S. November nonfarm payrolls spurred speculation the Fed may move by the middle of next year to boost rates from near zero now.

That trade was reversed however after Federal Reserve Chairman Ben Bernanke said late on Monday that interest rates would remain low for an extended period.

"Feels like a classic flight-to-quality," said Andrew Brenner, managing director of Guggenheim partners in New York.

London interbank offered rates for three-month euros were unchanged at 0.68 percent on Tuesday, bucking the downward trend in equivalent dollar and yen rates.

Benchmark interbank euro rates are likely to edge up into year-end as rising risk aversion over Greece's fiscal woes and ongoing concerns about Dubai's debt problems spur banks to hold onto cash, analysts said.

The two-year euro zone interest rate swap spread expanded to 51 basis points, its widest in three weeks after Fitch cut Greece's debt rating to BBB+ from A- with a negative outlook, undermining investor appetite for higher-yielding assets.

The spread is seen as a key measure of broader banking and financial market stress and a widening spread indicates some strain.

The two-year euro zone bond yield EU2YT=RR fell to its lowest in over a week while the U.S. T-bill rates fell as investors sought to park their cash in the perceived safety and liquidity of this paper.

"Events of the last few hours have hastened the strategy for investors moving down the curve towards very short-dated paper," said Kenneth Broux, markets economist at Lloyds TSB in London.

"On interbank lending, conditions are likely to be fairly tight, maybe there is a bigger reluctance to lend over year end, that's something to take into account and euro Libor could rise a few basis points going into year-end," he said.

However, some in the market reckon excess central bank liquidity, which has kept short-term money market rates pinned close to record lows, will be the more important driver, keeping those rates subdued as the year ends.

Underscoring that money markets remain bloated with excess cash, the ECB drained out just shy of 130 billion euros on Monday. The move was designed to rebalance the system at the end of its latest maintenance period. (Additional reporting by Emelia Sithole-Matarise in London and Emily Flitter in New York; Editing by James Dalgleish)