We investigate the effect of the hot CNO cycle breakout reaction 15O(α,γ)19Ne on the occurrence of type I X-ray bursts on accreting neutron stars. For frp . 0.1, where frp is a dimensionless factor by which we multiply the 15O(α,γ)19Ne reaction rate of Caughlan & Fowler (1988), our model predicts that bursts should occur only for accretion rates Ṁ below a critical value ≈ 0.3ṀEdd. This agrees w...