Thin polystyrene films were formed on polycrystalline platinum by styrene deposition followed by UV-initiated polymerization under cryogenic, ultrahigh-vacuum conditions. Temperature-programmed desorption (TPD) experiments showed that styrene chemisorbs weakly on the Pt surface. In the temperature region of 115-145 K, the adsorbed styrene films undergo a crystallization process that can be described by the Avrami equation. The polymerization rate increased with incident UV intensity, as expected, but was found to decrease with increasing temperature, most likely the result of competition between crystallization and polymerization. Ex-situ analysis of the resulting polystyrene films showed that high molecular weight polymer is formed. Finally, it is shown that the thickness can be reproducibly controlled by controlling the initial monomer dosage.