  The Pauli Exclusion Principle (PEP) appears from fundamental symmetries in
quantum field theories, but its physical origin is still to be understood.
High-precision experimental searches for small PEP violations permit testing
key assumptions of the Standard Model with high sensitivity. We report on a
dedicated measurement with Gator, a low-background, high-purity germanium
detector operated at the Laboratori Nazionali del Gran Sasso, aimed at testing
PEP-violating atomic transitions in lead. The experimental technique, relying
on forming a new symmetry state by introducing electrons into the pre-existing
electron system through a direct current, satisfies the conditions of the
Messiah-Greenberg superselection rule. No PEP violation has been observed, and
an upper limit on the PEP violation probability of $\beta^2/2 < 4.8 \cdot
10^{-29}$ (90% CL) is set. This improves the previous constraint from a
comparable measurement by more than one order of magnitude.
