We provide one of the first constraints on the combined infrared single-scattering albedo and opacity of Neptune's upper tropospheric cloud layer. For the observations, we used the adaptive optics system on the Lick Observatory's 3 m Shane Telescope (Mount Hamilton, California). The cloud layer is thought to be composed H(2)S of and extend up to 3.5-4.5 bars. Previously, the single-scattering albedo was measured in the range 0.2-0.94 mum and found to be extremely high (>0.8), but decreasing with increasing wavelength. Assuming an optically thick cloud, we find the best-Dt single-scattering albedo of a 3.5 bar layer to be at 0.23(-0.08)(+0.07) at 1.27 mum and 0.18(-0.04)(+0.03) at 1.56 mum. Uncertainties in the column density of haze above the cloud layer, and from deconvolution to remove contaminating light scattered by the point-spread function from infrared-bright features, indicate that the cloud could be even darker, but it is unlikely to be brighter than we report. The cloud particles could be brighter than we report if the total near-infrared opacity of the cloud is very low or the cloud's scattering phase function is significantly more forward-scattering at 1.2-1.6 mum than at 0.75 mum.