  Certain perturbative aspects of two-dimensional sigma models with (0,2)
supersymmetry are investigated. The main goal is to understand in physical
terms how the mathematical theory of ``chiral differential operators'' is
related to sigma models. In the process, we obtain, for example, an
understanding of the one-loop beta function in terms of holomorphic data. A
companion paper will study nonperturbative behavior of these theories.
