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Strain-engineering is a powerful means to tune the polar, structural, and electronic instabilities of incipient ferroelectrics. KTaO3 is near a polar instability and shows anisotropic superconductivity in electron-doped samples. Here, we demonstrate growth of high-quality KTaO3 thin films by molecular-beam epitaxy. Tantalum was provided by either a suboxide source emanating a TaO2 flux from Ta2O5 contained in a conventional effusion cell or an electron-beam-heated tantalum source. Excess potassium and a combination of ozone and oxygen (10% O3 + 90% O2) were simultaneously supplied with the TaO2 (or tantalum) molecular beams to grow the KTaO3 films. Laue fringes suggest that the films are smooth with an abrupt film/substrate interface. Cross-sectional scanning transmission electron microscopy does not show any extended defects and confirms that the films have an atomically abrupt interface with the substrate. Atomic force microscopy reveals atomic steps at the surface of the grown films. Reciprocal space mapping demonstrates that the films, when sufficiently thin, are coherently strained to the SrTiO3 (001) and GdScO3 (110) substrates.