A “quine” is a deterministic program that prints itself. In this essay, I will show you a “gauguine”: a probabilistic program that infers itself. A gauguine is repeatedly asked to guess its own source code. Initially, its chances of guessing correctly are of course minuscule. But as the gauguine observes more and more of its own previous guesses, it detects patterns of behavior and gains information about its inner workings. This information allows it to bootstrap self-knowledge, and ultimately discover its own source code. We will discuss how—and why—we might write a gauguine, and what we stand to learn by constructing one.