In response to the growing epidemic of obesity and diet-related chronic diseases, a number of governments are proposing taxes designed to reduce the consumption of unhealthy foods and thereby improve health outcomes. In this paper, I provide the first estimates of the effects of price changes in foods rich in sugar on the prevalence of obesity and diet-related chronic diseases, such as diabetes and hypertension. The analysis is made possible by rich longitudinal and nationally representative micro data on food prices and objective measures of health outcomes in Mexico from 1996-2010. I employ a unique barcoded level price dataset with product-specific nutritional information combined with two datasets on health outcomes: (1) a state-level administrative dataset and (2) an individual panel dataset. Exploiting plausibly exogenous within-state variation in prices over time, I show that a decrease in the price of sugar-rich foods significantly increases the prevalence of abdominal obesity, type 2 diabetes, and hypertension. In addition, the least healthy and most impatient individuals seem to be more responsive to price changes, suggesting that time preferences are an important mechanism driving the results. Overall, the effect of sugar prices on the incidence of chronic diseases is large. Since the signing of NAFTA, I estimate that the reduction in prices of sugar-rich foods explains 20 percent of the increase in diabetes.