A confident Chael is a good Chael. I'm unsure if Chael would beat Anderson.
Some people have said that Anderson has shown some weakness in defending takedowns, like in his fight against Travis Lutter. Two points against that idea: One, that fight happened years ago; and two, Anderson has since improved. Exhibit A: His fight against Dan Henderson.
To calculate Chael's odds against Anderson, a consideration about Anderson's fight with Hendo should be considered.
Would Chael defeat Hendo? Probably not. Hendo's wrestling may be somewhat better than Chael's--but Hendo's standing striking is much better than anything Chael has shown in the WEC or UFC. Hendo would probably TKO Chael in a late second round victory.
Anderson deftly beat Hendo. Chael would probably lose to Hendo. So, logic would say Chael would lose to Anderson. But, then again, this is MMA, and anything can happen. Gotta love that 'X' factor.