Chelsea has won the FA Cup seven times. It has also won the premier league four times. The premier league is the most competitive league in England.
3 times definitely
As of November 2011, Chelsea and Queens Park Rangers have met nine times in the Premier League.
Chelsea have won the premiere league four times once in 1950, twice with Mourinho and once with Anchelotti.
they have won it twice
Chelsea have won three Premier League titles in 2004,2005 and 2010
Chelsea Football Club has won the English Premier League three times ('04-'05, '05-'06, and '09-'10). Also, Chelsea won the first divison league cup in the 1954-1955 season, which was the top tier of English football before the creation of the English Premier League in 1992.
I guess by league one you mean the division called Coca-Cola Football League One, the third highest division, after the Premier League and Championship. Chelsea never won it. Chelsea have won the Premier League 3 times, in 1955, 2005 and 2006, and the Championship twice, in 1984 and 1989.