Surface plasmons in metal hole arrays have been studied extensively in the context of extraordinary optical transmission, but so far these arrays have not been studied as resonators for surface plasmon lasing at optical frequencies. We experimentally study a metal hole array with a semiconductor (InGaAs) gain layer placed in close (20\nm) proximity of the metal hole array. As a function of increasing pump power we observe an intense and spectrally narrow peak, with a clear threshold. This laser emission is donut shaped and radially polarized. Three experimental observations support that the system shows surface plasmon lasing. First, the full wavelength dispersion of the observed resonances can be understood using a single surface plasmon mode of the system. Second, the polarization of these resonances is as expected for surface plasmons. Third, the magnitude of the avoided crossing, which results from mode coupling at the holes, has a similar magnitude as found in simulations using surface plasmons.