Microwave heating of an aqueous solution of citric acid, boric acid and urea affords boron-doped carbon dots (C-dots) with ultrafine size (2-6 nm) and quasi-spherical shape. The new dots are freely dispersible in water providing stable, optically transparent dispersions with olive-green color. The optical properties of the dots were studied in respect to their photoluminescence and nonlinear optical response. Boron-doped C-dots exhibit absorption-emission features that strongly resemble the optical properties of conventional quantum dots with a strong blue fluorescence under UV excitation. Importantly, we demonstrate for the first time that boron doping in C-dots causes a significant enhancement of the nonlinear optical response compared to un-doped carbon dots. This result is in line with previous studies reporting a similar effect on the non-linear optical properties of boron-doped silicon nanocrystals.