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An area law is proved for the Renyi entanglement entropy of possiblydegenerate ground states in one-dimensional gapped quantum systems. Suppose ina chain of $n$ spins the ground states of a local Hamiltonian with energy gap$\epsilon$ are constant-fold degenerate. Then, the Renyi entanglement entropy$R_\alpha(0<\alpha<1)$ of any ground state across any cut is upper bounded by$\tilde O(\alpha^{-3}/\epsilon)$, and any ground state can be well approximatedby a matrix product state of subpolynomial bond dimension $2^{\tildeO(\epsilon^{-1/4}\log^{3/4}n)}$.

Area law in one dimension: Degenerate ground states and Renyi entanglement entropy