High-entropy oxide (HEO) superconductors have been developed since very recently. Different superconductors can be produced in the form of a high-entropy compound, including REBa₂Cu₃O_7−δ (REBCO). However, until now, mainly bulk samples (mostly in polycrystalline form) have been reported. In this work, the first CSD-grown high-entropy (HE) REBCO nanocomposite films were successfully synthesized. In particular, high-quality Gd_0.2Dy_0.2Y_0.2Ho_0.2Er_0.2Ba₂Cu₃O_7−δ nanocomposite films with 12 mol% BaHfO₃ nanoparticles were grown on SrTiO₃ substrates. The X-ray diffraction patterns show a near-perfect c-axis oriented grain growth. Both T_c and 77 K J^sf_c, 91.9 K and 3.5 MA cm⁻², respectively, are comparable with the values of the single-RE REBCO films. Moreover, at low temperatures, specifically at 30 K, the J_c values are larger than those of the single-RE samples. A transmission electron microscopy (TEM) study, including energy-dispersive X-ray spectroscopy (EDXS) measurements, reveals that the different RE³⁺ ions are distributed homogeneously in the matrix without forming clusters. This distribution causes point-like pinning centres that explain the superior performances of these samples at low temperatures. Although still seen as a proof-of-concept for the feasibility of preparing such films, these results demonstrate that the HE REBCO films are a promising option for the future fabrication of high-performance coated conductors. In the investigated B–T range, however, their J_c values are still lower than those of other, medium-entropy REBCO films, which shows that an optimization of the composition of the HE REBCO films is needed to maximize their performance.