The physical origin of fast radio bursts (FRBs) remains unclear. Finding multiwavelength counterparts of FRBs can provide a breakthrough for understanding their nature. In this work, we perform a systematic search for astronomical transients whose positions are consistent with FRBs. We find an unclassified optical transient AT2020hur (α = 01h58m00.ˢ750 ± 1″,
δ
=
65
°
43
′
00
.″
30
±
1
″
) that is spatially coincident with the repeating FRB 180916B (α = 01h58m00.ˢ7502 ± 2.3 mas,
δ
=
65
°
43
′
00
.″
3152
±
2.3
mas; Marcote et al. 2020). The chance possibility of the AT2020hur–FRB 180916B association is about 0.04%, which corresponds to a significance of 3.5σ. We develop a giant flare (GF) afterglow model to fit AT2020hur. Although the GF afterglow model can interpret the observations of AT2020hur, the derived kinetic energy of such a GF is at least three orders of magnitude larger than that of a typical GF, and a lot of fine-tuning and coincidences are required for this model. Another possible explanation is that AT2020hur might consist of two or more optical flares originating from the FRB source, e.g., fast optical bursts produced by the inverse Compton scattering of FRB emission. Besides, AT2020hur is located in one of the activity windows of FRB 180916B, which provides independent support for the association. This coincidence may be due to the optical counterparts being subject to the same periodic modulation as FRB 180916B, as implied by the prompt FRB counterparts. Future simultaneous observations of FRBs and their optical counterparts may help to reveal their physical origin.