An original constraint on the Hubble constant: h>74

5 pages, 1 figure. Submitted to MNRASThe Hubble parameter H0 is still not very well measured. Although the Hubble Key Project, Chandra and WMAP gave good estimates, the uncertainties remain quite large. In this brief report, we suggest an original and independent method to derive a lower limit on H0 using the absorption of very high energy gamma-rays by the cosmic infrared background. With conservative hypothesis, we obtain H0>74 km/s/Mpc at the 68% confidence level, which favors the upper end of the intervals allowed by dedicated experiments