Ultrathin MnPt films have been grown on Pt(001) single crystals by alternate deposition of Mn and Pt and studied in situ by grazing incidence x-ray diffraction. The growth mode and chemical order strongly depend on the deposition conditions. At room temperature, a 3D growth mode for Pt leads to a disordered and rough MnPt film. After annealing at 770 K, chemical order develops with the tetragonal axis oriented in the surface plane. At 570 K, Pt grows in a quasi layer-by-layer mode. For all depositions, and even after annealing, Mn remains essentially at the surface with negligible diffusion into bulk. As a consequence, the film deposited at 570 K is chemically ordered, with the tetragonal axis oriented mainly perpendicular to the surface. Coupled to ferromagnetic layers with in-plane (out-of-plane) anisotropy, these ultrathin ( ≈ 3 nm) MnPt films exhibit exchange bias properties and enhanced coercivity at low temperature.