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Deep optical observations contemporaneous with emission from the periodic FRB 180916.J0158+65

We present deep Apache Point Observatory optical observations within seconds of the outburst of the periodic fast radio burst (FRB) 180916.J0158+65 obtained on 3 September 2020. 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), we did not detect any transient optical emission at m_i=24.7~mag (3-sigma) from 2.2 to 1938.1 seconds 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 >1e44 erg and the circumburst density was >1e4 cm-3.