  We define harmonic maps between sub-Riemannian manifolds by generalizing
known definitions for Riemannian manifolds. We establish conditions for when a
horizontal map into a Lie group with a left-invariant metric structure is a
harmonic map. We show that sub-Riemannian harmonic maps can be abnormal or
normal, just as sub-Riemannian geodesics. We illustrate our study by presenting
the equations for harmonic maps into the Heisenberg group.
