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Recent changes in labor arrangements have increased interest in estimating and understanding the value of job flexibility. We leverage a large natural field experiment at Uber to create exogenous variation in expected market wages across individuals and over time. Combining this experiment with high frequency panel data on wages and individual work decisions, we document how labor supply responds to exogenous changes in expected market wages in a setting with virtually no restrictions on drive labor allocation. We find that there is i) systematic heterogeneity in labor supply responses both across drivers and within a driver over time, ii) significant fixed costs of beginning a shift, and iii) high rider demand when it is costly for drivers to work. These three findings motivate a model of labor supply with heterogeneous preferences over work schedules, adjustment costs, and statistical dependence between market wages and the costs of driving. We recover the labor supply elasticities and reservation wages of this dynamic labor supply model via a combination of experimental estimates and other data moments. We then perform counterfactual analyses that allow us to examine how preference heterogeneity and adjustment costs influence the responses of workers' to wage incentives as well as infer drivers' willingness to pay for the ability to customize and adjust their work schedule. We also show that a static approach to the driver's dynamic problem delivers materially different estimates of workers' labor supply elasticities and their value of job flexibility.