Pulsed laser deposition has been used to grow Pt(621) thin films having a chiral orientation on SrTiO3(621) substrates. Films were deposited over a range of conditions, then characterized for their crystallinity and epitaxy using x-ray diffraction and for their surface morphologies using atomic force microscopy (AFM). Films deposited at 600 °C grew epitaxially, but with an island growth mode. Pt deposited at 250 °C displayed smooth surfaces but did not grow epitaxially. A three-step process wherein films were seeded at 600 °C, deposited at 250 °C, and postannealed was shown to result in excellent epitaxial growth and flat surface morphologies. Films grown using the three-step process exhibited excellent epitaxy, having the orientation relationship (621)Pt||(621)SrTiO3:Pt||SrTiO3. When postannealed at 800 °C, they exhibited flat surfaces (rms≈20 Å) having long terraces separated by steps running along the expected  direction of the SrTiO3(621) substrate. Films postannealed at 600 °C were flatter (rms≈10 Å) with no evident step directionality. The SrTiO3(621) substrates were observed to be extremely flat (rms≈2 Å) and to have morphologically featureless surfaces, as expected for a (621) surface. The good crystalline quality of the SrTiO3 substrate surface is considered to drive the growth of the chirally oriented heteroepitaxial Pt films. Similarities and differences between Pt growth on chiral surfaces and on low-index achiral surfaces are discussed.