Theories of personal identity try to explain what the identity of a person necessarily consists in, but frequently leave open what kind of necessity is at issue. This paper is concerned with conceptual necessity. It proposes an analysis of the concept of personal identity in terms of a definite description. The analysis coheres with out judgments about clear cases and explains why cases of division seem indeterminate. The apparent indeterminacy results from attempting to apply a definite description to a situation in which more than one object would satisfy the description. The definite description analysis also explains the strengths of the influential no-branching theory, while avoiding the problems with that view. The no-branching theory is in effect a second-order analysis, i.e., a combination of the definite description analysis of personal identity plus a Russellian analysis of the definite description