© 2018 authors. The measured value of the Higgs quartic coupling λ is peculiarly close to the critical value above which the Higgs potential becomes unstable, when extrapolated to high scales by renormalization group running. It is tempting to speculate that there is an anthropic reason behind this near-criticality. We show how an axionic field can provide a landscape of vacuum states in which λ scans. These states are populated during inflation to create a multiverse with different quartic couplings, with a probability distribution P that can be computed. If P is peaked in the anthropically forbidden region of Higgs instability, then the most probable universe compatible with observers would be close to the boundary, as observed. We discuss three scenarios depending on the Higgs vacuum selection mechanism: decay by quantum tunneling, by thermal fluctuations, or by inflationary fluctuations.