Ultrasonic composite oscillator measurements of the mechanical relaxation in RBa(2)Cu(3)O(7-8) arising from oxygen hopping in the basal chain layer show enhancements in oxygen mobility of 20, 50, and 100 times for R = gadolinium, neodymium, and lanthanum, respectively, above that for R = yttrium. The use of the larger rare earths offers a practical solution to the major problem of slow oxygen diffusion in single crystals and bulk, dense material for wires and melt-textured monolithic bodies.