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We present photometric and spectroscopic observations of SN 2013aa and SN 2017cbv, two nearly identical type Ia supernovae (SNe Ia) in the host galaxy NGC 5643. The optical photometry has been obtained using the same telescope and instruments used by the Carnegie Supernova Project. This eliminates most instrumental systematics and provides light curves in a stable and well-understood photometric system. Having the same host galaxy also eliminates systematics due to distance and peculiar velocity, providing an opportunity to directly test the relative precision of SNe Ia as standard candles. The two SNe have nearly identical decline rates, negligible reddening, and remarkably similar spectra and, at a distance of $\sim 20$ Mpc, are ideal as potential calibrators for the absolute distance using primary indicators such as Cepheid variables. We discuss to what extent these two SNe can be considered twins and compare them with other supernova "siblings" in the literature and their likely progenitor scenarios. Using 12 galaxies that hosted 2 or more SNe~Ia, we find that when using SNe~Ia, and after accounting for all sources of observational error, one gets consistency in distance to 3 percent.