Introducing an epitaxial growth technique called corner overgrowth, we fabricate a quantum confinement structure consisting of a high-mobility GaAs/AlGaAs heterojunction overgrown on top of an ex situ cleaved substrate corner. The resulting corner-junction quantum-well heterostructure effectively bends a two-dimensional electron system (2DES) at an atomically sharp 90° angle. The high-mobility 2DES demonstrates fractional quantum Hall effect on both facets. Lossless edge-channel conduction over the corner confirms a continuum of 2D electrons across the junction, consistent with Hartree calculations of the electron distribution. This growth technique differs distinctly from cleaved-edge overgrowth and enables a complementary class of embedded quantum heterostructures.