Y. Dong Northwestern/CIERA, C. D. Kilpatrick, W. Fong, A. P. Curtin, S. Opoku, B. C. Andersen, A. M. Cook, T. Eftekhari, E. Fonseca, B. M. Gaensler, R. C. Joseph, J. F. Kaczmarek, L. A. Kahinga, V. Kaspi, A. E. Lanman, M. Lazda, C. Leung, K. W. Masui, D. Michilli, K. Nimmo, A. Pandhi, A. B. Pearlman, M. Sammons, P. Scholz, V. Shah, K. Shin, K. Smith

We present a systematic search for past supernovae (SNe) and other historical optical transients at the positions of fast radio burst (FRB) sources to test FRB progenitor systems. Our sample comprises 83 FRBs detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and its KKO Outrigger, along with 93 literature FRBs representing all known well-localized FRBs. We search for optical transients coincident in position and redshift with FRBs and find no significant associations within the 5-sigma FRB localization uncertainties except for a previously identified potential optical counterpart to FRB 20180916B. By constraining the timescale for SN ejecta to become transparent to FRB emission, we predict that it takes at least 6-10 years before the FRB emission can escape. From this, we infer that approximately 7% of matched optical transients, up to 30% of currently known SNe, and up to 40% of core-collapse SNe could have an observable FRB based on timescales alone. We derive the number of new, well-localized FRBs required to produce one FRB-SN match by chance, and find it will take ~ 22,700 FRBs to yield one chance association at the projected CHIME/FRB Outrigger detection rate. Looking forward, we demonstrate redshift overlap between SNe detected by the upcoming Vera C. Rubin Observatory and CHIME/FRB Outrigger FRBs, indicating the prospect of an increase in potential associations at redshift z < 1. Our framework is publicly available, flexible to a wide range of transient timescales and FRB localization sizes, and can be applied to any optical transient populations in future searches.