  We calculate multi-instanton effects in a three-dimensional gauge theory with
N=8 supersymmetry and gauge group SU(2). The k-instanton contribution to an
eight-fermion correlator is found to be proportional to the Gauss-Bonnet-Chern
integral of the Gaussian curvature over the centered moduli-space of charge-k
BPS monopoles, \tilde{M}_{k}. For k=2 the integral can be evaluated using the
explicit metric on \tilde{M}_{2} found by Atiyah and Hitchin. In this case the
integral is equal to the Euler character of the manifold. More generally the
integral is the volume contribution to the index of the Euler operator on
\tilde{M}_{k}, which may differ from the Euler character by a boundary term. We
conjecture that the boundary terms vanish and evaluate the multi-instanton
contributions using recent results for the cohomology of \tilde{M}_{k}. We
comment briefly on the implications of our result for a recently proposed test
of M(atrix) theory.
