  In this article, we propose an experimental scheme for observation of a
quantum anomaly---quantum-mechanical symmetry breaking---in a two-dimensional
harmonically trapped Bose gas. The anomaly manifests itself in a shift of the
monopole excitation frequency away from the value dictated by the
Pitaevskii-Rosch dynamical symmetry [L. P. Pitaevskii and A. Rosch, Phys. Rev.
A, 55, R853 (1997)]. While the corresponding classical Gross-Pitaevskii
equation and the derived from it hydrodynamic equations do exhibit this
symmetry, it is---as we show in our paper---violated under quantization. The
resulting frequency shift is of the order of 1% of the carrier, well in reach
for modern experimental techniques. We propose using the dipole oscillations as
a frequency gauge.
