From unicellular ciliates to the respiratory epithelium, carpets of cilia display metachronal waves, long-wavelength phase modulations of the beating cycles, which theory suggests may arise from hydrodynamic coupling. Experiments have been limited by a lack of organisms suitable for systematic study of flagella and the flows they create. Using time-resolved particle image velocimetry, we report the discovery of metachronal waves on the surface of the colonial alga Volvox carteri, whose large size and ease of visualization make it an ideal model organism for these studies. An elastohydrodynamic model of weakly coupled compliant oscillators, recast as interacting phase oscillators, reveals that orbit compliance can produce fast, robust synchronization in a manner essentially independent of boundary conditions, and offers an intuitive understanding of a possible mechanism leading to the emergence of metachronal waves.