Chiral magnets with topologically nontrivial spin order such as Skyrmions have generated enormous interest in both fundamental and applied sciences. We report broadband microwave spectroscopy performed on the insulating chiral ferrimagnet Cu2OSeO3. For the damping of magnetization dynamics we find a remarkably small Gilbert damping parameter of about 1x10^4 at 5 K. This value is only a factor of 4 larger than the one reported for the best insulating ferrimagnet yttrium iron garnet at room temperature. We detect a series of sharp resonances and attribute them to confined spin waves in the mm-sized samples. Considering the small damping, insulating chiral magnets turn out to be promising candidates when exploring non-collinear spin structures for high frequency applications.