Using new as well as known results on dimerized quantum spin chains with frustration, we are able to infer some properties on the low-energy spectrum of the O (3) Nonlinear Sigma Model with a topological θ-term. In particular, for sufficiently strong coupling, we find a range of values of θ where a singlet bound state is stable under the triplet continuum. On the basis of these results, we propose a new renormalization group flow diagram for the Nonlinear Sigma Model with a θ-term.