The author analyses the upper tail of the distribution of tourism supply in Portugal from 2002 to 2009, using data from the Instituto Nacional de Estatística database. Tourism supply is defined in terms of the lodging capacity of hotel establishments in about 250 tourist destinations. The paper shows that the empirical distribution of tourism supply in Portugal is heavy-tailed and consistent with a power law behaviour in its upper tail. Such behaviour seems to be stable over the years, provided that, for the time horizon covered by the data sets, the scaling parameter is always close to the value of two. The power law hypothesis is tested positively through the use of graphical and analytical methods. Cooperation among stakeholders and the enlargement of the base for tourism supply are the main policy implications drawn from the power law analysis to avoid the threat of a fall in tourist arrivals in Portugal.