Recently a physical medium was fabricated in which both the effective permittivity and the effective permeability are simultaneously negative over a restricted frequency range. Thus, in this frequency range such a medium is "left--handed", and is characterized by a negative refractive index. In this paper we study the scattering of p-and s-polarized electromagnetic waves from, and their transmission through, a slab of a left--handed medium whose illuminated surface is a one-dimensional randomly rough surface. We assume that the surface profile function is a single-valued function of the coordinate in the mean plane of the surface that is normal to its grooves and ridges, and constitutes a zero-mean, stationary, Gaussian random process. In the frequency range we are interested in, the electric and magnetic excitations give rise to p- and s-polarized surface polaritons, Brewster modes, and waveguide modes in the slab. The reflectivity and the transmissivity of such a slab as a function of the angle of incidence displays structure associated with the existence of a Brewster angle in both polarizations and the existence of a critical angle for total internal reflection in both polarizations. The presence of surface roughness leads to a shift of the Brewster angle, the sign of which depends on the existence or nonexistence of surface or guided waves at the frequency of the incident field.