  In the present paper we demonstrate that there exists a new type of neutron
stars in the tensor-multi-scalar theories of gravity. We call this new type of
neutron stars topological neutron stars. In addition to the standard
characteristics of the usual neutron stars the topological neutron stars are
also characterized by a topological charge. We numerical construct explicit
examples of topological neutron stars in tensor-multi-scalar theories whose
target space is $\mathbb{S}^3$. Besides the topological charge the topological
neutron stars also exhibit other attractive features which can place them among
the realistic compact objects that could exist in Nature. For example they
possess zero scalar charge and thus evades the strong binary pulsar constraints
on the dipole scalar radiation.
