Reduced dimensionality and interlayer coupling in van der Waals materials gives rise to fundamentally different electronic(1), optical(2) and many-body quantum(3-5) properties in monolayers compared with the bulk. This layer-dependence permits the discovery of novel material properties in the monolayer regime. Ferromagnetic order in two-dimensional materials is a coveted property that would allow fundamental studies of spin behaviour in low dimensions and enable new spintronics applications(6-9). Recent studies have shown that for the bulk-ferromagnetic layered materials Crl(3), (ref. (9) ) and Cr2Ge2Te6 (ref. (10)), ferromagnetic order is maintained down to the ultrathin limit at low temperatures. Contrary to these observations, we report the emergence of strong ferromagnetic ordering for monolayer VSe2, a material that is paramagnetic in the bulk(11,12). Importantly, the ferromagnetic ordering with a large magnetic moment persists to above room temperature, making VSe2 an attractive material for van der Waals spintronics applications.