We report a colloidal synthesis approach to CsPbBr3 nanoplatelets (NPLs). The nucleation and growth of the platelets, which takes place at room temperature, is triggered by the injection of acetone in a mixture of precursors that would remain unreactive otherwise. The low growth temperature enables the control of the plate thickness, which can be precisely tuned from 3 to 5 monolayers. The strong two-dimensional confinement of the carriers at such small vertical sizes is responsible for a narrow PL, strong excitonic absorption, and a blue shift of the optical band gap by more than 0.47 eV compared to that of bulk CsPbBr3. We also show that the composition of the NPLs can be varied all the way to CsPbBr3 or CsPbI3 by anion exchange, with preservation of the size and shape of the starting particles. The blue fluorescent CsPbCl3 NPLs represent a new member of the scarcely populated group of blue-emitting colloidal nanocrystals. The exciton dynamics were found to be independent of the extent of 2D confinement in these platelets, and this was supported by band structure calculations.