It has long been conjectured that hydrodynamic interactions between beating eukaryotic flagella underlie their ubiquitous forms of synchronization; yet there has been no experimental test of this connection. The biflagellate alga Chlamydomonas is a simple model for such studies, as its two flagella are representative of those most commonly found in eukaryotes. Using micromanipulation and high-speed imaging, we show that the flagella of a C. reinhardtii cell present periods of synchronization interrupted by phase slips. The dynamics of slips and the statistics of phase-locked intervals are consistent with a low-dimensional stochastic model of hydrodynamically coupled oscillators, with a noise amplitude set by the intrinsic fluctuations of single flagellar beats.