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Magneto-optical Kerr effect microscopy is used to show that monolayer chromium triiodide is an Ising ferromagnet with out-of-plane spin orientation.Since the discovery of graphene1, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin-valley coupling2, Ising superconductors3,4,5 that can be tuned into a quantum metal6, possible Mott insulators with tunable charge-density waves7, and topological semimetals with edge transport8,9. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered10,11,12,13,14; such a crystal would be useful in many technologies from sensing to data storage15. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem16. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals17,18,19. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect20, whereas in trilayer CrI3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics12, and van der Waals engineering to produce interface phenomena15.