A group of glass compositions in the Li2O—Al2O3—SiO2—B2O3 family that can be chemically strengthened in single or multiple ion exchange baths containing at least one of NaNO3 and KNO3 for a short time (2-4 hours) to develop a deep depth of layer (DOL). In some instances, the DOL is at least 70 μm; in others, at least about 100 μm. The ion exchanged glasses have a high damage resistance (indentation fracture toughness ranging form greater than 10 kgf to greater than 50 kgf) that is better than or at least comparable to that of sodium aluminosilicate glasses.