The formalism for a relativistic open-shell CCSD(T) method is presented and implemented in a computer program, RELCCSD. The code can be used for calculations with 2- or 4-component relativistic reference wave functions and allows a full inclusion of the spin-orbit coupling. The code is interfaced to the MOLFDIR program system, We illustrate its use with nb initio calculations of the fine structure splittings of Cl, FO, ClO, O-2(+), and O-2(-). The triples correction is found to make a large contribution to the Cl atom splitting, which is within 23 cm(-1), of the experimental value. The molecular results are within 4 cm(-1) of the experimental values where these are available, The value for FO is predicted to be -195+/-4 cm(-1), in good agreement with experiment.