We used CHILI, the Chicago Instrument for Laser Ionization, a new resonance ionization mass spectrometer developed for isotopic analysis of small samples, to analyze strontium, zirconium, and barium isotopes in 22 presolar silicon carbide grains. Twenty of the grains showed detectable strontium and barium, but none of the grains had enough zirconium to be detected with CHILI. Nine grains were excluded from further consideration since they showed very little signals (<1000 counts) for strontium as well as for barium. Among the 11 remaining grains, we found three X grains. The discovery of three supernova grains among only 22 grains was fortuitous, because only ∼1% of presolar silicon carbide grains are type X, but was confirmed by silicon isotopic measurements of grain residues with NanoSIMS. While one of the X grains showed strontium and barium isotope patterns expected for supernova grains, the two other supernova grains have 87Sr/86Sr < 0.5, values never observed in any natural sample before. From their silicon isotope ratios, the latter two grains can be classified as X2 grains, while the former grain belongs to the more common X1 group. The differences of these grains in strontium and barium isotopic composition constrain their individual formation conditions in Type II supernovae.