Abstract Fast radio bursts (FRBs) are a class of highly energetic, mostly extragalactic radio transients lasting for ∼milliseconds. While over 600 FRBs have been published so far, their origins are presently unclear, with some theories for extragalactic FRBs predicting accompanying high-energy emission. In this work, we use the Canadian Hydrogen Intensity Mapping Experiment (CHIME) Fast Radio Burst (CHIME/FRB) Project to explore whether any FRB-like radio emission coincides in space and time with 81 gamma-ray bursts (GRBs) detected between 2018 July 17 and 2019 July 8 by Swift/BAT and Fermi/GBM. We do not find any statistically significant coincident pairs within 3σ of each other’s spatial localization regions and within a time difference of up to one week. In addition to searching for spatial matches between known FRBs and known GRBs, we use CHIME/FRB to constrain FRB-like (∼1–10 ms) radio emission before, at the time of, or after the reported high-energy emission at the position of 39 GRBs. For short gamma-ray bursts (SGRBs), we constrain the radio flux in the 400–800 MHz band to be under a few kJy for ∼5.5–12.5 hr post-high-energy burst. We use these limits to constrain models that predict FRB-like prompt radio emission after SGRBs. For long gamma-ray bursts, we constrain the radio flux to be under a few kJy from ∼6 hr pre-high-energy burst to ∼12 hr post-high-energy burst.