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We report on the growth of stoichiometric, single-crystal YCrO₃ epitaxial thin films on (001) SrTiO₃ substrates using pulsed laser deposition. X-ray diffraction and atomic force microscopy reveal that the films grew in a layer-by-layer fashion with excellent crystallinity and atomically smooth surfaces. Magnetization measurements demonstrate that the material is ferromagnetic below 144 K. The temperature dependence of dielectric permittivity shows a characteristic relaxor-ferroelectric behavior at <i>T</i>_C = 375–408 K. A dielectric anomaly at the magnetic transition temperature indicates a close correlation between magnetic and electric order parameters in these multiferroic YCrO₃ films. These findings provide guidance to synthesize rare-earth, chromite-based multifunctional heterostructures and build a foundation for future studies on the understanding of magnetoelectric effects in similar material systems.