DyCrO3 (DCO) belongs to the family of rare-earth chromites, some members of which exhibit magnetoelectric multiferroic properties. This work characterizes the dielectric tunability in DCO, which is typically, for conventional ferroelectrics, found to maximize near the ferroelectric to paraelectric transition. Two films of DCO were fabricated via a hybrid solution synthesis route on different substrates: one on single crystalline (001) LaAlO3 (LAO) and the other on (001) LAO coated with a conducting LaNiO3 (LNO) layer. The synthesis method resulted in films with both out-of-plane and in-plane texture in the DCO. The lattice mismatch strain between film and substrate caused a slight increase in the Neel temperature of the DCO film on LAO. Transmission electron microscopy images of the DCO film on the LNO/LAO revealed the epitaxial relationship between these phases. The temperature dependence of the relative permittivity showed diffused transition and a frequency dispersion similar to what is observed in typical relaxor ferroelectrics. Isothermal dielectric constant versus dc electric field measurements showed an electric field tunable relative permittivity (i.e., tunability). This tunability reached a broad plateau near the Neel temperature. Such maxima in dielectric tunability are typically observed near a ferroelectric–paraelectric transition, and its proximity to the magnetic ordering temperature in DCO indicates magnetically driven ferroelectricity in this material.