Individuals can claim Social Security at any age from 62 to 70 although most claim at 62 or soon thereafter. Those who delay claiming receive increases that are approximately actuarially fair. We show that expected present value calculations substantially understate both the optimal claim age and the losses resulting from early claiming because they ignore the value of the additional longevity insurance acquired as a result of delay. Using numerical optimization techniques, we illustrate that for plausible preference parameters, the optimal age for non-liquidity constrained single individuals and married men to claim benefit is between 67 and 70. We calculate that Social Security Equivalent Income, the amount by which benefits payable at suboptimal ages must be increased so that a household is indifferent between claiming at those ages and the optimal combination of ages, can be as high as 19.0 percent.