The unicellular protist Chlamydomonas reinhardtii swims toward light sources using an anterior pair of flagella for propulsion and an eye spot that serves as a directional photoreceptor. Free-swimming Chlamydomonas rotate about the long axis of the cell, and the varying signal of the eye spot is thought to make one flagellum dominant in its beating, re-orienting the cell toward the light source. While dominance is broadly accepted, the underlying nature of dominance-changes in force, frequency, or synchrony-has yet to be determined. It has also yet to be directly demonstrated that this model accounts for phototaxis. We used a laser trap to capture free-swimming Chlamydomonas and measure the propulsive forces and beat frequencies generated by the flagella in the presence and absence of a directional light source. A 3D computational model of Chlamydomonas motility was developed using parameters measured in the laser trap. The data suggest that the most functionally significant change in the flagella in response to light is a waveform change in the trans flagellum that increases its lateral beat strength. The computational model shows that subtle changes in lateral beat strength are necessary and sufficient for phototaxis, and explains the conserved rotational rate of Chlamydomonas.