  We unveil the signature of many-body interference across dynamical regimes of
the Bose-Hubbard model. Increasing the particles' indistinguishability enhances
the temporal fluctuations of few-body observables, with a dramatic
amplification at the onset of quantum chaos. By resolving the exchange
symmetries of partially distinguishable particles, we explain this
amplification as the fingerprint of the initial state's coherences in the
eigenbasis.
