  We propose an equation that describes M2-branes ending on M5-branes, and
which generalizes the description of the D1-D3 system via Nahm's equation. The
simplest solution to this equation constructs the transverse geometry in terms
of a fuzzy three sphere. We show that the solution passes a number of
consistency checks including a consistent reduction to the D1-D3 system, a
calculation of the energy of the system, matching to the self-dual string
solution in the M5-brane world volume, and a study of simple fluctuations about
the ground state configuration. We write down certain terms in the effective
action of multiple membranes, which includes a sextic scalar coupling.
