Deep Optical Observations Contemporaneous with Emission from the Periodic FRB 180916.J0158+65

We present deep Apache Point Observatory optical observations within seconds of radio emission from the periodic fast radio burst (FRB) 180916.J0158+65 obtained on 2020 September 3. FRB 180916.J0158+65 is located in a nearby spiral galaxy 150 Mpc away and has an "active phase" with a well-measured period of approximately 16.3 days. Targeting the FRB at the peak of its expected active phase and during a recent 30 minute observing window by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) in which a radio burst was detected, we did not detect any transient optical emission at ${m}_{i}$ ≈ 24.7 mag (3σ) from 2.2 to 1938.1 s after the burst arrival time in optical bands (corrected for dispersion). Comparing our limiting magnitudes to models of a synchrotron maser formed in the circumburst environment of FRB 180916+J0158.65, we constrain scenarios where the burst energy was $\gt {10}^{44}$ erg and the circumburst density was >10⁴ cm^-3.