Using high-resolution x-ray scattering, we have demonstrated the existence of quenched disordered charge stripes in a single crystal of La5/3Sr1/3NiO4 at low temperatures. Above the second-order transition critical scattering was observed due to fluctuations into the charge stripe phase. The charge stripes are shown to be two dimensional in nature both by measurements of their correlation lengths (xi(a) approximate to 185 Angstrom, xi(b) = 400 Angstrom, and xi(c) approximate to 25 Angstrom) and by the critical exponents of the charge strip transition. The charge stripe orderings did not develop long-range order even at low temperatures, indicating that the charge stripes are disordered and that the length scale of the disorder is quenched.