  We apply the Hamiltonian formulation of teleparallel theories of gravity in
2+1 dimensions to a circularly symmetric geometry. We find a family of
one-parameter black hole solutions. The BTZ solution fixes the unique free
parameter of the theory. The resulting field equations coincide with the
teleparallel equivalent of Einstein's three-dimensional equations. We calculate
the gravitational energy of the black holes by means of the simple expression
that arises in the Hamiltonian formulation and conclude that the resulting
value is identical to that calculated by means of the Brown-York method.
