4 times
1954-55, 2004-05, 2005-06, 2009-10
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i don't know about right now, but the end of season 05/06 and the beginning of 06/07 Chelsea went 42 matches unbeaten, which is almost as good as Arsenal's 49 matches.
As of 21st September 2008 it is now 85 home league games unbeaten since the 2-1 to Arsenal in February 2004.