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Chain sequences are positive sequences {a_n} of the forma_n=g_n(1−g_n−1) for a nonnegative sequence {g_n}. This concept was introduced by Wall in connection with continued fractions. In his monograph on orthogonal polynomials, Chihara conjectured that ifa_n⩾1 4 for eachnthen ∑(a_n−1 4 )⩽1 4 . We prove this conjecture and give other precise estimates fora_n. We also characterize the chain sequences {a_n} whose terms are greater than 1 4 . We show connections to Jacobi matrices and orthogonal polynomials. In particular, we characterize the maximal chain sequences in terms of integrability properties of the spectral measure of the associated Jacobi matrix.