Under most circumstances, not getting into data skew, bad column choices, etc.
In fact, having an index on C1 or an index on C1 and C2 as keys would be effective duplicates of C1, C2, C3 as keys. I would strongly, in most situations, insert several caveats, recommend against that.
However, like has already be stated, check the execution plan to be sure. You may be in one of the edge cases. We, and you, can't possibly know without testing.