RadixZip is a block compression technique for token streams. It introduces RadixZip Transform, a linear time algorithm that rearranges bytes using a technique inspired by radix sorting. For appropriate data, RadixZip Transform is analogous to the Burrows-Wheeler Transform used in bzip2, but is both simpler in operation and more effective in compression. In addition, RadixZip Transform can take advantage of correlations between token streams with no computational overhead. Experiments over practical data show that for common token streams, RadixZip is superior to bzip2.