In addition to spintronics another motivation for exploring ferromagnetic two-dimensional materials is for biomedical applications such as magnetic labeling and hyperthermia treatment of tumors. Unfortunately, the widely studied Mn-containing monolayer is not biocompatible, although it is ferromagnetic. Here using first principles calculations combined with Monte Carlo simulations based on the Ising model, we systematically study a class of 2D ferromagnetic monolayers CrX3 (X = Cl, Br, I). The feasibility of exfoliation from their layered bulk phase is confirmed by the small cleavage energy and high in-plane stiffness. Spin-polarized calculations, combined with self-consistently determined Hubbard U that accounts for strong correlation energy, demonstrate that CrX3 (X = Cl, Br, I) monolayers are ferromagnetic and that Cr is trivalent and carries a magnetic moment of 3 μ(B); the resulting Cr(3+) ions are biocompatible. The corresponding Curie temperatures for CrCl3, CrBr3 and CrI3 are found to be 66, 86, and 107 K, respectively, which can be increased to 323, 314, and 293 K by hole doping. The biocompatibility and ferromagnetism render these Cr-containing trihalide monolayers unique for applications.