  The destruction of the Kondo effect in a local-moment metal can lead to a
topological non-Fermi-liquid phase, dubbed fractionalized Fermi liquid, with
spinon-type excitations and an emergent gauge field. We demonstrate that, if
the latter displays an internal $\pi$-flux structure, a chiral heavy-fermion
metal naturally emerges near the Kondo-breakdown transition. Utilizing a parton
mean-field theory describing the transition between a conventional heavy Fermi
liquid and a U(1) fractionalized Fermi liquid, we find a novel intermediate
phase near the transition whose emergent flux pattern spontaneously breaks both
translation and time-reversal symmetries. This phase is an orbital
antiferromagnet, and we discuss its relevance to pertinent experiments.
