Over one third of the uninsured adults in the U.S. below retirement age are between 19 and 29 years old. Young adults, especially men, often go without insurance, even when buying it is mandatory and sometimes even when it is a low cost employment benefit. This paper proposes a new form of health insurance targeted at this group—the “Young Invincibles”—those who (wrongly) believe that they don’t need health insurance because they won’t get sick. Our proposal offers a cash bonus to those who turn out to be right in their belief that they did not really need health insurance. The concept comes from the tontine life insurance that fueled the rise of the U.S. insurance industry in the late 19th Century. A largely forgotten casualty of the 1906 pacification of the life insurance industry, the tontine idea holds great promise for making health insurance attractive to the invincibles today. The tontine feature frames the health insurance purchase as a smart investment, rather than a way to spend money for something the customer does not think he needs. Tontines make insurance more attractive to the uninsured, without wasting funds by subsidizing those who are already covered. We identify a particular class of individuals (the invincibles), show how a specific cognitive bias accounts for their irrational behavior, and design an insurance mechanism (tontines or deferred dividends) to overcome the effects of this bias. The final sections of the paper offer an empirically calibrated pricing demonstration for a tontine health policy and an analysis of the legality of tontines in this context.