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I can find no evidence of a Baillie link with Clan Chattan, though some Baillies of Lowland origin settled in the Highlands, Inverness and Ross. The name has not died our in Scotland but flourishes there. As for a clan connection the Baillies seem able to stand on their own, having their own tartan and a long history of their own as a lowland surname.
http://www.electricscotland.com/history/nation/baillie.htm
However, the suggestion that Baillie could derive from the name Balliol can be ignored, Marc's is the accepted explanation.