Specific heat measurements have been performed on a single crystal sample of the copper chain compound Cu(3-Clpy)(2)(N-3)(2) which is regarded as the spin-1/2 ferromagnetic-ferromagnetic-antiferromagnetic-antiferromagnetic (F-F-AF-AF) tetramer chain. The temperature dependence of specific heat at zero magnetic field shows a gradual decrease upon cooling below about 6 K and reaches a finite value at low temperatures before showing a peak around 0.5 K. The latter behavior except the peak resembles that of the spin-1/2 Heisenberg ferromagnetic chain, which probably arises from the low lying excitation with a ferromagnetic feature in this system. Numerical calculation (exact diagonalization method) tip to 12 spins of the specific heat for the spin-1/2 F-F-AF-AF Heisenberg chain reproduces this behavior and shows a tendency of the peak around 0.5 K. The origin of the peak and the specific heat in a magnetic field is discussed.