The discovery rate of fast radio bursts ( FRBs ) is increasing dramatically thanks to new radio facilities .
Meanwhile , wide-field instruments such as the 47 deg ^ { 2 } Zwicky Transient Facility ( ZTF ) survey the optical sky to study transient and variable sources .
We present serendipitous ZTF observations of the CHIME repeating source FRB 180916.J0158+65 , that was localized to a spiral galaxy 149 Mpc away and is the first FRB suggesting periodic modulation in its activity .
While 147 ZTF exposures corresponded to expected high-activity periods of this FRB , no single ZTF exposure was at the same time as a CHIME detection .
No > 3 \sigma optical source was found at the FRB location in 683 ZTF exposures , totalling 5.69 hours of integration time .
We combined ZTF upper limits and expected repetitions from FRB 180916.J0158+65 in a statistical framework using a Weibull distribution , agnostic of periodic modulation priors .
The analysis yielded a constraint on the ratio between the optical and radio fluences of \eta \lesssim 200 , corresponding to an optical energy E _ { opt } \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 ) = 1 hr ^ { -1 } and 1.2 \pm 1.1 FRB occurring during exposures taken in high-activity windows .
The constraint can be improved with shorter per-image exposures and longer integration time , or observing FRBs at higher Galactic latitudes .
This work demonstrated how current surveys can statistically constrain multi-wavelength counterparts to FRBs even without deliberately scheduled simultaneous radio observation .