We have demonstrated that single point diamond turning can be used to generated high optical quality finished surfaces on a new organic nonlinear crystal, L-arginine phosphate (LAP). The proper choice of cutting conditions can produce surfaces with less than 5 angstroms rms surface roughness. Local softening or melting near the cutting tool tip may play a key role in the machining process by ensuring that material is removed by ductile cutting rather than brittle fracture. At the same time, the low melting temperature of LAP makes lubrication and cooling especially important to prevent extensive melting and tool fouling. In spite of the presence of a weak cleavage plane in LAP, the surface quality is relatively insensitive to crystallographic orientation. Tool wear is apparently negligible, so that surface flatness is governed by the stability of the diamond turning machine. Data on residual subsurface strain and preliminary measurements of the optical damage thresholds of diamond turned LAP surfaces will be presented.