The activity in CO oxidation of regular arrays of Pd clusters, in the size range 5 -180 atoms, supported on alumina has been studied by 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. The TOF increases with size. Below about 20 atoms, the TOF increases rapidly and for larger clusters it grows slowly and reaches at 180 atoms a value close to those obtained on bulk single crystals. The size effect is explained by the smaller activity of Pd atoms in contact with the alumina support.