I propose to use laser heating both for the substrate and the thermal evaporation sources in a vacuum chamber operating at pressures from XHV to values where the mean free path of the particles approaches or slightly exceeds the source-substrate distance. The concept combines the advantages of the molecular beam epitaxy (MBE) and pulsed laser deposition (PLD) methods to allow ultrapure deposition with continuous stoichiometry variation at high background pressures of arbitrary gases or molecular beams. Theory and preliminary experiments suggest that this setup is capable of growing complex oxides such as SrTiO3 in the adsorption-controlled regime, similar to GaAs, in a background of molecular oxygen. This regime is neither accessible to MBE nor to PLD, making this laser epitaxy approach a unique tool to explore new growth regimes with the potential to fabricate structures such as modulation-doped heterostructures with low levels of background impurities that are impossible to synthesize with the current techniques. The technological simplicity and exceedingly compact size of the deposition chamber enable easy and rapid switching between different materials systems and the efficient synthesis of new materials that involve corrosive constituents. In contrast to PLD, the method may be scaled in a straightforward manner to large substrate sizes, providing a direct path from research to mass production.