© 2014 American Physical Society. Q balls are nontopological solitonic solutions to a wide class of field theories that possess global symmetries. Here we show that in these same theories there also exists a tower of novel composite Q-ball solutions where, within one composite Q ball, positive and negative charges coexist and swap at a frequency lower than the natural frequency of an individual Q ball. These charge-swapping Q balls are constructed by assembling Q balls and anti-Q balls tightly such that their nonlinear cores overlap. We explain why charge-swapping Q balls can form and why they swap charges.