Many tests have rejected the implications of the consumption CAPM for data on U.S. asset returns. All of the tests, though, assume that the pricing errors satisfy the Central Limit Theorem. I provide empirical evidence that the marginal distributions of the pricing errors are so heavy-tailed that they do not satisfy the Central Limit Theorem. Using recent work on jackknifing, I construct a method of testing asset pricing models with heavy-tailed errors. Using this procedure, I find that the consumption CAPM is not rejected by annual U.S. data.