Two-dimensional (2D) semiconductors with suitable direct band gaps, high carrier mobility, and excellent open-air stability are especially desirable for material applications. Herein, we show theoretical evidence of a new phase of a copper(i) sulfide (Cu2S) monolayer, denoted δ-Cu2S, with both novel electronic properties and superior oxidation resistance. We find that both monolayer and bilayer δ-Cu2S have much lower formation energy than the known β-Cu2S phase. Given that β-Cu2S sheets have been recently synthesized in the laboratory (Adv. Mater.2016, 28, 8271), the higher stability of δ-Cu2S than that of β-Cu2S sheets suggests a high possibility of experimental realization of δ-Cu2S. Stability analysis indicates that δ-Cu2S is dynamically and thermally stable. Notably, δ-Cu2S exhibits superior oxidation resistance, due to the high activation energy of 1.98 eV for the chemisorption of O2 on δ-Cu2S. On its electronic properties, δ-Cu2S is a semiconductor with a modest direct band gap (1.26 eV) and an ultrahigh electron mobility of up to 6880 cm2 V-1 s-1, about 27 times that (246 cm2 V-1 s-1) of the β-Cu2S bilayer. The marked difference between the electron and hole mobilities of δ-Cu2S suggests easy separation of electrons and holes for solar energy conversion. Combination of these novel properties makes δ-Cu2S a promising 2D material for future applications in electronics and optoelectronics with high thermal and chemical stability.