  We demonstrate that the observed cosmological excess of matter over
antimatter may originate from a heavy QCD axion that solves the strong CP
problem but has a mass much larger than that given by the Standard Model QCD
strong dynamics. We investigate a rotation of the heavy QCD axion in field
space, which is transferred into a baryon asymmetry through weak and strong
sphaleron processes. This provides a strong cosmological motivation for heavy
QCD axions, which are of high experimental interest. The viable parameter space
has an axion mass $m_a$ between 1~MeV and 10 GeV and a decay constant $f_a <
10^5$ GeV, which can be probed by accelerator-based direct axion searches and
observations of the cosmic microwave background.
