  The fast radio bursts (FRBs) 110220 and 140514 were detected at telescope
pointing locations within 9 arcmin of each other over three years apart, both
within the same 14.4 arcmin beam of the Parkes radio telescope. Nevertheless,
they generally have not been considered to be from the same source because of a
vastly different dispersion measure (DM) for the two bursts by over $380\,{\rm
pc\,cm^{-3}}$. Here we consider the hypothesis that these two FRBs are from the
same neutron star embedded within a supernova remnant (SNR) that provides an
evolving DM as the ejecta expands and becomes more diffuse. Using such a model
and the observed DM change, it can be argued that the corresponding SN must
have occurred within $\approx10.2$ years of FRB 110220. Furthermore,
constraints can be placed on the SN ejecta mass and explosion energy, which
appear to require a stripped envelope (Type Ib/c) SN and/or a very energetic
explosion. A third FRB from this location would be even more constraining,
allowing the component of the DM due to the SNR to be separated from the
unchanging DM components due to the host galaxy and intergalactic medium. In
the future, if more FRBs are found to repeat, the sort of arguments presented
here can be used to test the young neutron star progenitor hypothesis for FRBs.
