The first Two-Face story from Detective Comics #66 skips a month and continues from its cliff-hanger in Detective #68 (August 1942). Two-Face flips a coin (with a green hand!) to determine if he will lead a life of crime or try to get help. The coin stands on its edge so he lets fate decide. Of course fate decides he should be a super-criminal!
In a sub-plot, Harvey Dent goes to visit his ex-fiance and she shrieks in horror as the wax on the scarred side of his face melts, resulting in this rather horrifying panel: