  Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds since
they are not holomorphic. Instead, \kahler normal coordinates (KNC) can be
defined as holomorphic coordinates. We prove that KNC transform as a
holomorphic tangent vector under holomorphic coordinate transformations, and
therefore that they are natural extensions of RNC to the case of \kahler
manifolds. The KNC expansion provides a manifestly covariant background field
method preserving the complex structure in supersymmetric nonlinear sigma
models.
