The chiral Abelian Higgs model contains an interesting class of solitons found by Rubakov and Tavkhelidze. These objects carry non-zero fermion number NF (or Chern-Simons number NCS, what is the same because of the chiral anomaly) and are stable for sufficiently large NF. In this paper we study the properties of these anomalous solitons. We find that their energy-versus-fermion-number ratio is given by E ∼ NCS 3 / 4 or E ∼ NCS 2 / 3 depending on the structure of the scalar potential. For the former case we demonstrate that there is a lower bound on the soliton energy, which reads E ≥ c NCS 3 / 4, where c is some parameter expressed through the masses and coupling constants of the theory. We construct the anomalous solitons numerically accounting both for Higgs and gauge dynamics and show that they are not spherically symmetric. The thin wall approximation valid for macroscopic solutions with NCS ≫ 1 is discussed as well. © 2007 Elsevier B.V. All rights reserved.