TREASURIES-Prices gain after slightly dovish Fed statement

(Recasts with Fed statement; Adds quotes, updates prices)

* Fed dovish on inflation, hints at balance sheet reduction

* Treasury sells $34 bln five-year notes to strong demand

* Three-month T-bill yields elevated on debt ceiling concerns

NEW YORK, July 26 (Reuters) - U.S. Treasury prices gained on Wednesday after the Federal Reserve indicated that it is likely to begin paring its balance sheet in the coming months and struck a slightly dovish tone on inflation. The U.S. central bank said it expected to start winding down its massive holdings of bonds "relatively soon." It also noted that both overall inflation and a measure of underlying price gains had declined and said it would "carefully monitor" price trends. They were very balanced, said Aaron Kohli, an interest rate strategist at BMO Capital Markets in New York. They acknowledged inflation weakness, which was the dovish part of the statement, and they also kept a fairly tight leash on the market by basically implying that they are ready to taper relatively soon. Many analysts and traders expect the Fed to announce its balance sheet reduction plans at its September meeting. Futures traders are pricing in a 50-percent chance that the Fed will raise rates at its December meeting, down from 52 percent before the statement, according to the CME Group's FedWatch Tool.

Benchmark 10-year notes gained 11/32 in price to

yield 2.29 percent, down from 2.33 percent on Tuesday. The Treasury Department sold $34 billion in five-year notes to solid demand on Wednesday, the second sale of $88 billion in new coupon-bearing supply this week. A $26 billion sale of two-year notes on Tuesday was also well bid. Fund managers, foreign central banks and other indirect bidders took their biggest share at five-year government note auction in seven months. The United States will also sell $28 billion in seven-year notes on Thursday.

Yields on one-month Treasury bills rose above 1

percent. If the bill yields end the day above that level it will mark the first time since before Lehman Brothers collapsed in September 2008 that the entire U.S. yield curve has yielded over 1 percent.

Yields on three-month Treasury bills that are due

in October were also elevated on concerns that payments on debt due in the month will be delayed if Congress fails to raise the debt ceiling. The Congressional Budget Office said last month that Congress would need to increase the debt limit by early to mid-October to avoid a default.

Yields on Treasury bills that mature on Oct. 26

last traded at 1.14 percent after rising to 1.20 percent on Tuesday, the highest level since October 2008.

(Editing by Lisa Shumaker)