Two branches of integrable open quantum-group invariant quantum spin chains are known. For one branch (), a complete Bethe ansatz solution has been proposed. However, the other branch () has so far resisted solution. In an effort to address this problem, we consider here the simplest case n  =  1. We propose a Bethe ansatz solution, which however is not complete, as it describes only the transfer-matrix eigenvalues with odd degeneracy. We also consider a proposal for the missing eigenvalues.