The activity in CO oxidation of regular arrays of Pd clusters, in the size range of 5-180 atoms, supported on alumina has been studied by using a molecular beam method. The Pd clusters are grown on a nanostructured ultrathin alumina film on Ni3Al(111) providing a hexagonal array of clusters with a narrow size distribution. The steady state turnover frequency (TOF) is measured as a function of the mean cluster size. On average the TOF increases with size. Below about 20 atoms, the TOF increases rapidly and for larger clusters it grows slowly and reaches a value close to those obtained on bulk single crystals at 180 atoms. The size effect is explained by the smaller activity of Pd atoms in contact with the alumina support.