Housing quality, both in terms of the physical structure and neighborhood characteristics, is positively associated with health outcomes. I examine the Housing Choice Voucher (HCV) program as a possible means of improving the health of recipients who would otherwise participate in place-based assistance programs such as public housing, or rent without a subsidy in the private market. Under three weak and plausible assumptions—voucher holders have weakly worse average potential health outcomes than non-recipients (non-positive monotone treatment selection); receiving a voucher does not result in strictly poorer health (monotone treatment response); on average, potential health outcomes are positively related to reported income (monotone instrumental variable)—I obtain nonparametric bounds on the average treatment effect of HCV on the health of individuals in recipient households using nationally-representative data from the 2018 Survey of Income and Program Participation (SIPP). My preferred estimates indicate that the causal effect is positive and statistically significant, with the likelihood of good or better self-reported health status increased by at least 4.8 percentage points and at most 21.3 percentage points. I also estimate that the probability of not having been hospitalized over the previous year is increased between 0.1 and 18.4 percentage points, though the effect is not statistically distinguishable from zero at conventional levels. Among Black members of voucher households, I estimate a larger lower bound for the effect on self-reported health of 11.7 percentage points, hinting that the effect on health is potentially larger for this subpopulation.