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High quality thin films of high temperature superconducting La/sub 1.85/Sr/sub 0.15/CuO/sub 4/ have been grown using pulsed laser deposition on LaSrAlO/sub 4/ buffer layers on  SrTiO/sub 3/ substrates. An ozone/oxygen mixture was used during the cooling of the films from the deposition temperature. The zero-resistance superconducting transition temperature T/sub c/ was 39 K and the critical current density J/sub c/ was over 10/sup 6/ A/cm/sup 2/ at 4.2 K for 800 /spl Aring/ thin films. The resistivity was found to depend linearly on temperature with a resistivity ratio /spl rho/(300 K)//spl rho/p(50 K) of 4.5 and an intercept at T=0 of /spl sim/30 /spl mu//spl Omega/cm.