  We study the $SU(2)$ Principal Chiral Model (PCM) in the presence of an
integrable $\eta$-deformation. We put the theory on $\mathbb{R}\times S^1$ with
twisted boundary conditions and then reduce the circle to obtain an effective
quantum mechanics associated with the Whittaker-Hill equation. Using resurgent
analysis we study the large order behaviour of perturbation theory and recover
the fracton events responsible for IR renormalons. The fractons are modified
from the standard PCM due to the presence of this $\eta$-deformation but they
are still the constituents of uniton-like solutions in the deformed quantum
field theory. We also find novel $SL(2,\mathbb{C})$ saddles, thus strengthening
the conjecture that the semi-classical expansion of the path integral gives
rise to a resurgent transseries once written as a sum over Lefschetz thimbles
living in a complexification of the field space. We conclude by connecting our
quantum mechanics to a massive deformation of the $\mathcal{N}=2~$ $4$-d gauge
theory with gauge group $SU(2)$ and $N_f=2$.
