High quality In0.52Ga0.48As, InP, and In0.52Ga0.4gAs/InP single quantum wells were grown on GaAs (100) by gas-source molecular beam epitaxy (GSMBE) with a 2 mum thick InxGa1-xAs buffer layer where x was linearly graded from 0 to 0.52. Reflection high-energy electron diffraction patterns and specular beam intensity oscillations showed that the growth mode of In0.52Ga0.48As and InP were layer by layer despite the lattice mismatch (DELTAa/a = 3.8%) between InP and GaAs. Photoluminescence line widths at 10 K of a 1-mum thick InP and a 5-nm wide In0.52Ga0.48As/InP single quantum well are 4.9 and 10 meV, respectively, which are comparable to the values measured from similar structures grown lattice matched on an InP substrate (3.5 and 7 meV, respectively) by the same GSMBE system. The quantum-well luminescence intensity is also comparable to lattice-matched samples.