* Yellen says considerable slack in U.S. economy, jobs market
* Dollar index down after 3 days of gains
* Euro firms against yen, dollar (Recasts following Yellen comments, adds quotes, late prices)
NEW YORK, March 31 (Reuters) - The dollar dropped on Monday, ending a string of gains against other major currencies as the U.S. central bank chief said bond buying and low interest rates aimed at boosting the U.S. economy would likely be kept in place for some time.
Already helped to a three-week high against the yen by softer-than-forecast eurozone inflation data, the euro climbed against the dollar to a high of $1.3806 before easing to $1.3777 for a rise of 0.17 percent against the greenback.
The U.S. dollar index of major currencies, coming off three days of gains, was down 0.11 percent to 80.089 in late afternoon New York trade after dipping below 80 in the wake of a speech in Chicago by Federal Reserve Chair Janet Yellen.
Yellen said there was "considerable" slack in America's jobs market and economy and easy-money programs were likely to continue for some time.
"The result of her remarks was to weaken the dollar generally," said Lane Newman, director of foreign exchange at ING Capital Markets, adding that the talk had confirmed for many investors Yellen's easy-credit ideas.
The dollar had been mostly rising since March 19, when Yellen surprised global markets with possible hints at a news conference that the Fed may wind up its bond-buying program faster than expected and begin raising interest rates as soon as early 2015.
In late New York trading, the euro was ahead 0.60 percent against the yen at 142.20 yen.
The euro ended little changed against the British pound after going as high as 0.8298 pound on trading driven by speculation that euro zone inflation will not be soft enough to spur more monetary easing by the ECB.
Europe's central bankers worry that a euro approaching a $1.40 level, not seen since 2011, would aggravate deflationary forces and hurt economic recovery.
"It will take action by the ECB for the euro to decline," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. "Investors want actions."
The market also looks doubtful about any action by the ECB to ease policy further this week.
Data on Monday showed inflation sank to just 0.5 percent in March but, as Bundesbank chief Jens Weidmann underlined on Saturday, much of the fall has been due to one-off drops in energy and food prices over which the ECB has little control. (Additional reporting by Patrick Graham in London; Editing by James Dalgleish and Dan Grebler)