This paper introduces the concept of the utility copula, a function which incorporates the dependence information between (or among) variables of a utility function. A utility copula is a natural extension of the ordinary (probability) copula and the Lévy copula, but relates to a different domain, typically bounded from below in its variables. Thus the utility measure does not go to zero at minus infinity, as in the case of a probability measure, nor to zero at plus infinity, as in the case of a Lévy measure. This qualification requires the non-trivial implementation of the Fundamental Theorem of the Calculus for valuation of the utility copula. Accordingly, issues arise concerning the equivalence of restricted vs. marginal utility functions, leading to recognition of the distinction between regular and irregular utility functions, defined within. The development proceeds to examples of utility copulas, and further to the construction of bivariate (or multivariate) utility functions from a utility copula and marginal utility functions. Further, the paper presents specific tests of necessity and sufficiency on candidate utility copulas, drawn from the spaces of ordinary and Lévy copulas, and provided with marginal utility functions, to assure that a constructed bivariate function be a utility function. Suggestions for applications, and conclusions, follow.