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The discovery rate of fast radio bursts (FRBs) is increasing dramaticallythanks to new radio facilities. Meanwhile, wide-field instruments such as the47 deg$^2$ Zwicky Transient Facility (ZTF) survey the optical sky to studytransient and variable sources. We present serendipitous ZTF observations ofthe CHIME repeating source FRB 180916.J0158+65, that was localized to a spiralgalaxy 149 Mpc away and is the first FRB suggesting periodic modulation in itsactivity. While 147 ZTF exposures corresponded to expected high-activityperiods of this FRB, no single ZTF exposure was at the same time as a CHIMEdetection. No $>3\sigma$ optical source was found at the FRB location in 683ZTF exposures, totalling 5.69 hours of integration time. We combined ZTF upperlimits and expected repetitions from FRB 180916.J0158+65 in a statisticalframework using a Weibull distribution, agnostic of periodic modulation priors.The analysis yielded a constraint on the ratio between the optical and radiofluences of $\eta \lesssim 200$, corresponding to an optical energy $E_{\rmopt} \lesssim 3 \times 10^{46}$ erg for a fiducial 10 Jy ms FRB (90%confidence). A deeper (but less statistically robust) constraint of $\eta\lesssim 3$ can be placed assuming a rate of $r(>5$ Jy ms)= hr$^{-1}$ and$1.2\pm 1.1$ FRB occurring during exposures taken in high-activity windows. Theconstraint can be improved with shorter per-image exposures and longerintegration time, or observing FRBs at higher Galactic latitudes. This workdemonstrated how current surveys can statistically constrain multi-wavelengthcounterparts to FRBs even without deliberately scheduled simultaneous radioobservation.

Zwicky Transient Facility constraints on the optical emission from the nearby repeating FRB 180916.J0158+65