  We prove a first Kronecker limit formula for cofinite discrete subgroups of
SL$(2,\mathbb{C})$, also called Kleinian groups, generalizing a method of
Goldstein over SL$(2,\mathbb R)$. The proof uses the Fourier expansion of
Eisenstein series, leading to an analogue of the logarithm of the Dedekind eta
function, and whose transformation law produces a function analogous to one
related to Dedekind sums. We derive several basic properties of this new
function.
