  It is well-known that exact enumerations of close-packed dimers can be
carried out for two-dimensional lattices. While details of results are now
known for most lattices, due to the unique nature of the lattice structure,
there has been no complete analysis for the kagome lattice. Here we derive the
close-form expression $(1/3) \ln (4 x y z)$ for the free energy of close-packed
dimers on the kagome lattice, where $x,y,z$ are dimer weights. We use two
different approaches, the Kasteleyn method of evaluating a Pfaffian and an
alternative vertex model formulation. Both methods lead to the same final
expression. The correlation function between two dimers at a distance equal or
greater than two lattice spacings is found to vanish identically.
