A pristine Rb3C60 single crystal with larger than millimeter dimensions was prepared by reaction of rubidium vapor with a seed-grown C-60 Single crystal (which exhibited remarkably sharp x-ray-diffraction peaks). A narrow superconducting transition width Delta T-c (5-85 % diamagnetic shielding) of the Rb3C60 Single crystal is less than 1 K. The onset of the transition was at a temperature, T-c=30.0 K. Measurements of temperature dependence of the zero-field-cooled and field-cooled de magnetization (using ten applied magnetic fields up to 5.0 T) are reported here. These and magnetization vs field data at different temperatures (ranging from 2 to 29 K) have been used to determine thermodynamic superconducting parameters, including the lower [H-c1(T)] and upper [H-c2(T)] critical fields, the Ginsburg-Landau coherence length xi, and the London or Ginzburg-Landau penetration depth, lambda. These are significantly different from those extracted from similar data in the literature for powder specimens. Hysteresis and magnetic relaxation measurements have been used to determine the nominal critical current density J(c)(H,T) and the effective-pinning potential U-eff(J,H), respectively.