I nominate Jack Silver's proof that, if the generalized continuum hypothesis is false, then the first counterexample cannot be a singular cardinal of uncountable cofinality. In the first place, the result was, as far as I know, totally unexpected. The general feeling was that Easton's results on violations of GCH at regular cardinals should extend to singular cardinals. Secondly, the proof was an unexpected mixture of combinatorial set theory and nonstandard models. (Later, other proofs were found that avoid the nonstandard models.)