Critical current densities of over 1.8×106 A/cm2 at 4.2 °K and 150 kG have been achieved in Nb3Al tapes rapidly quenched from the liquid state at rates of 105–106 °C/sec. The superconducting transition temperature is about 16 °K, indicating a relatively high degree of order, and increases to 18.4 °K upon annealing at 750 °C. The observed microstructure depends sensitively on the quenching rate and consists of small submicron grains surrounded by a thin boundary layer of different composition. The grain size is roughly inversely proportional to the temperature gradient during quenching. The quoted critical current densities, the highest observed to date in any superconductor, should be regarded as a lower limit of the material critical value imposed by the heating problems due to the contact resistance.