Integrated third-harmonic generators enable on-chip wavelength conversion translating telecom signals to the visible spectrum. Despite the desirable functionality, the device performance is susceptible to phase distortions. Here, we present a design method of compensating the Kerr-induced distortions in third-harmonic generation. The design method yields a chirped Bragg grating theoretically improving the conversion efficiency by ∼30 dB. We envision the design method will pave the way for demonstrating efficient infrared-to-visible upconversion in silicon nitride chips.