Chelsea have won 6 league trophies - 4 first division and 2 second division awards between 1950 and 2010. They have also won the FA cup 7 times, the FA community cup 4 times, the Football league cup another 4 times and have twice won the full members' cup. This means that their total number of domestic trophies is 23 so far.
They also have a total of 5 international trophies. These include the UEFA champions' league, which they won in 2011; the UEFA Europea league, which they won the following year; two victories in the UEFA cup winners' cup, in 1970 and 1997; and in 1988 they won the UEFA Super cup.
Chelsea are an old and well established football club, having been founded in 1905. They didn't in fact win a major championship until their first league victory which was in 1955, but have had regular successes since then.