We report density-functional-theory calculations of the electronic band structures and optical absorption spectra of two-dimensional crystals of Ga2X2 (X= S, Se, and Te). Our calculations show that all three two-dimensional materials are dynamically stable indirect-band-gap semiconductors with a sombrero dispersion of holes near the top of the valence band. We predict the existence of Lifshitz transitions—changes in the Fermi-surface topology of hole-doped Ga2X2—at hole concentrations nS=7.96×1013 cm−2, nSe=6.13×1013 cm−2, and nTe=3.54×1013 cm−2.