Drug overdoses involving opioid analgesics have increased dramatically since 1999, representing one of the United States' top public health crises. Opioids have legitimate medical functions, but improving access may increase abuse rates even among those not prescribed the drugs given that opioids are frequently diverted to nonmedical use. We have little evidence about the causal relationship between increased medical access to opioids and spillovers resulting in abuse. We use the introduction of the Medicare Prescription Drug Benefit Program (Part D) as a large and differential shock to the geographic supply of opioids. Part D increased opioid utilization for the 65+ population, and we show that this increase in utilization led to significant growth in the overall supply of opioids in high elderly share states relative to low elderly share states. This relative expansion in opioid supply resulted in an escalation in opioid-related substance abuse treatment admissions and opioid-related mortality among the Medicare-ineligible population, implying meaningful spillovers to individuals who did not experience any change in prescription drug benefits. The evidence suggests that increased opioid supply is associated with economically-important levels of diversion for nonmedical purposes. Our estimates imply that a 10% increase in medical opioid distribution leads to a 7.4% increase in opioid-related deaths and a 14.1% increase in substance abuse treatment admission rates for the Medicare-ineligible population.