We have synthesized unique colloidal nanoplatelets of the ferromagnetic two-dimensional (2D) van der Waals material CrI3 and have characterized these nanoplatelets structurally, magnetically, and by magnetic circular dichroism spectroscopy. The isolated CrI3 nanoplatelets have lateral dimensions of ~25 nm and ensemble thicknesses of only ~4 nm, corresponding to just a few CrI3 monolayers. Magnetic and magneto-optical measurements demonstrate robust 2D ferromagnetic ordering in these nanoplatelets with Curie temperatures similar to those observed in bulk CrI3, despite the strong spatial confinement. These data also show magnetization steps akin to those observed in micron-sized few-layer 2D sheets and associated with concerted spin-reversal of individual CrI3 layers within few-layer van der Waals stacks. Similar data have also been obtained for CrBr3 and anion-alloyed Cr(I1-xBrx)3 nanoplatelets. These results represent the first example of laterally confined 2D van der Waals ferromagnets of any composition. The demonstration of robust ferromagnetism at nanometer lateral dimensions opens new doors for miniaturization in spintronics devices based on van der Waals ferromagnets.