We discuss multichain effects in salt-free polyampholyte solutions of finite concentration and find that the existing single-chain theories are limited to exponentially small concentrations, if the sample contains chains with net charges of both signs. We show that charged polyampholytes have a strong tendency to form neutral complexes and to precipitate. Neutral samples, where the average net charge of the chains is exactly zero, phase separate at exponentially small concentrations. The supernatant is dominated by neutral unimers or clusters that form spherical globules and its polymer concentration c(dil) similar to exp(-(N) over tilde(2/3)) is independent of the total polymer concentration. For non-neutral samples, on the other hand, the free counterions accumulate in the supernatant together with the most strongly oppositely charged unimers, if the system is concentrated beyond the onset of phase separation. The dilute phase then consists of elongated globules and has a concentration proportional to the total polymer concentration.