The delayed response of law enforcement to calls for service has become a hot button issue when evaluating police department performance. While it is often assumed that faster response times could play an important role in quelling potentially violent incidents, to date there is no empirical evidence to support this claim. In this paper, we measure the effect of police response time on the likelihood that an incident results in an injury. To overcome the endogeneity between more severe calls being assigned higher priority, which requires a faster response, we take several steps. First, we focus on a subset of calls for service categorized as ``Major Disturbance - Violence" that all receive the same priority level. Second, we instrument for police response time with the number of vehicles within a 2.5 mile radius of the call at the time it is received by the call center. When controlling for beat & time of day fixed effects, this instrumenting strategy allows us to take advantage of the geographical constraints faced by a dispatcher when assigning officers to an incident. In contrast to the OLS estimates, our two-stage least squares analysis establishes a strong causal relationship whereby increasing response time increases the likelihood that an incident results in an injury. The effect is concentrated among female callers, suggesting that faster response time could potentially play an important role in reducing injuries related to domestic violence.