Precision cosmology with Type Ia supernovae (SNe Ia) makes use of the fact that SN Ia luminosities depend on their light-curve shapes and colours. Using Supernova Legacy Survey (SNLS) and other data, we show that there is an additional dependence on the global characteristics of their host galaxies: events of the same light-curve shape and colour are, on average, 0.08mag (~4.0{sigma}) brighter in massive host galaxies (presumably metal-rich) and galaxies with low specific star formation rates (sSFR).