Kinesin is a two-headed, ATP-driven motor protein that moves processively along microtubules in discrete steps of 8 nm, probably by advancing each of its heads alternately in sequence. Molecular details of how the chemical energy stored in ATP is coupled to mechanical displacement remain obscure. To shed light on this question, a force clamp was constructed, based on a feedback-driven optical trap capable of maintaining constant loads on single kinesin motors. The instrument provides unprecedented resolution of molecular motion and permits mechanochemical studies under controlled external loads. Analysis of records of kinesin motion under variable ATP concentrations and loads revealed several new features. First, kinesin stepping appears to be tightly coupled to ATP hydrolysis over a wide range of forces, with a single hydrolysis per 8-nm mechanical advance. Second, the kinesin stall force depends on the ATP concentration. Third, increased loads reduce the maximum velocity as expected, but also raise the apparent Michaelis-Menten constant. The kinesin cycle therefore contains at least one load-dependent transition affecting the rate at which ATP molecules bind and subsequently commit to hydrolysis. It is likely that at least one other load-dependent rate exists, affecting turnover number. Together, these findings will necessitate revisions to our understanding of how kinesin motors function.