The formation of methyl radicals into densely packed two-dimensional islands on the Cu(111) surface is directly observed for the first time by scanning tunneling microscopy (STM). It is shown that chemisorbed CH3(ads) molecules tend to aggregate into (root3 x root3) R30degrees structure in 2D islands at any coverage up to one saturation monolayer. The island sizes depend on the amount of gaseous exposure, and at a given exposure, the sizes are found to decrease when the surface temperature is raised to near the reaction temperature of CH3(ads). The adsorbate islanding behavior can be correlated with the first-order reaction kinetics in the generation of long-chain alkene products detected in the thermal desorption. From this and other related studies on methyl-solid interactions, we infer that the islanding phenomenon may be quite general in catalytic systems.