Atomically-thin layered van der Waals crystals represent ideal material systems in the ultimate two-dimensional (2D) limit. Among all layered materials, high-temperature superconductors stand out for their fundamental importance in material research and potential impact on future technology. Here, we developed a fabrication process that enabled us to produce intrinsic monolayer crystals of high-temperature superconductor Bi₂Sr₂CaCu₂O_8+δ (Bi-2212; here monolayer refers to a half unit cell) and probe their transport properties. The lack of dimensionality effect on superconducting transition temperature T_c defies expectations from Mermin-Wagner theorem; it also sharply contrasts with much reduced T_c in conventional superconductors in 2D limit. Being atomically thin, monolayer Bi-2212 offers unprecedented tunability over its doping and disorder level across the superconductor-insulator transition (SIT). Finite size scaling analysis at SIT provides a unified picture for disparate observations in cuprate systems. Our results establish monolayer Bi-2212 as an ideal platform for studying high-temperature superconductivity and other strongly correlated phenomena in 2D.