In this paper I demonstrate that, contrary to the standard interpretations, William Whewell's view of scientific method is neither that of the hypothetico-deductivist nor that of the retroductivist. Rather, he offers a unique inductive methodology, which he calls “discoverers' induction.” After explicating this methodology, I show that Kepler's discovery of his first law of planetary motion conforms to it, as Whewell claims it does. In explaining Whewell's famous phrase about “happy guesses” in science, I suggest that Whewell intended a distinction between “inductions,” which can be empirically verified, and “mere hypotheses”—or guesses—which cannot. Finally, I argue that Whewell's discoverers' induction is a view worthy of our attention today, because it avoids a number of problems faced by prominent alternative methodologies.