We experimentally realize a robust real-time random number generator by differentially comparing the signal from a chaotic semiconductor laser and its delayed signal through a 1-bit analog-to-digital converter. The probability density distribution of the output chaotic signal based on the differential comparison method possesses an extremely small coefficient of Pearson's median skewness (1.5 × 10⁻⁶), which can yield a balanced random sequence much easily than the previously reported method that compares the signal from the chaotic laser with a certain threshold value. Moveover, we experimently demonstrate that our method can stably generate good random numbers at rates of 1.44 Gbit/s with excellent immunity from external perturbations while the previously reported method fails.