  We calculate and analyze Feshbach resonance spectra for ultracold
Yb($^1$S$_0$) + Yb($^3$P$_2$) collisions as a function of an interatomic
potential scaling factor $\lambda$ and external magnetic field. We show that,
at zero field, the resonances are distributed randomly in $\lambda$, but that
signatures of quantum chaos emerge as a field is applied. The random zero-field
distribution arises from superposition of structured spectra associated with
individual total angular momenta. In addition, we show that the resonances in
magnetic field in the experimentally accessible range 400 to 2000~G are
chaotically distributed, with strong level repulsion that is characteristic of
quantum chaos.

Atomic Physics;Quantum Gases;Chaotic Dynamics