We report the optical identification of four Balmer-dominated supernova remnants (SNRs) in the Large Magellanic Cloud. Both the Balmer-dominated spectra and the presence of a broad Hα component in one remnant can be understood in terms of a very high velocity non-radiative shock encountering gas which is partially neutral, as proposed originally by Chevalier and Raymond to account for the similar spectra of the galactic remnants, Tycho and SN1006. From a consideration of the optical and X-ray luminosities of the SNR with broad Hα emission, we infer that the fraction of neutral gas in the medium is ≲ 30%. Radio observations of the LMC remnants show that their surface brightnesses are anomalously low; this could be intrinsic to the supernova themselves, or a result of their environment. Finally, we argue that the four SNRs all resulted from Type I supernovae, in which case they are the first such remnants to be identified outside the Galaxy.