We propose and experimentally realize a new kind of bound states in the continuum (BICs) in a class of systems constructed by coupling multiple identical one-dimensional chains, each with inversion symmetry. In such systems, a specific separation of the Hilbert space into a topological and a nontopological subspace exists. Bulk-boundary correspondence in the topological subspace guarantees the existence of a localized interface state which can lie in the continuum of extended states in the nontopological subspace, forming a BIC. Such a topological BIC is observed experimentally in a system consisting of coupled acoustic resonators.