The electron affinity of the rare gas element 118 is calculated by the relativistic coupled cluster method based on the Dirac-Coulomb-Breit Hamiltonian. A large basis set (34s26p20d14f9g6h4i) of Gaussian-type orbitals is used. The external 40 electrons are correlated. Inclusion of both relativity and correlation yields an electron affinity of 0.056 eV, with an estimated error of 0.01 eV. Nonrelativistic or uncorrelated calculations give no electron affinity for the atom.