The Milagrito collaboration recently reported evidence for emission of very high energy gamma rays in the TeV range from one of the BATSE gamma-ray bursts, GRB 970417a. Here I discuss possible interpretations of this result. Taking into account the intergalactic absorption of TeV gamma rays by the cosmic infrared background, I found that the detection rate (one per 54 gamma-ray bursts [GRBs] observed by the Milagrito) and energy fluence can be consistently explained with the redshift of this GRB at z approximately 0.7 and the isotropic total energy in the TeV range, ETeV,iso greater, similar1054 ergs. This energy scale is not unreasonably large, but interestingly similar to the maximum total GRB energy in the sub-MeV range observed to date for GRB 990123. On the other hand, the energy emitted in the ordinary sub-MeV range becomes EMeV,iso approximately 1051 ergs for GRB 970417a, which is much smaller than the total energy in the TeV range by a factor of about 10(3). I show that the proton-synchrotron model of GRBs provides a possible explanation for these observational results. I also discuss some observational signatures expected in future experiments from this model.