  We study chiral deformations of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric
gauge theories obtained by turning on $\tau_J \,{\rm tr} \, \Phi^J$
interactions with $\Phi$ the ${\cal N}=2$ superfield. Using localization, we
compute the deformed gauge theory partition function $Z(\vec\tau|q)$ and the
expectation value of circular Wilson loops $W$ on a squashed four-sphere. In
the case of the deformed ${\cal N}=4$ theory, exact formulas for $Z$ and $W$
are derived in terms of an underlying $U(N)$ interacting matrix model replacing
the free Gaussian model describing the ${\cal N}=4$ theory. Using the AGT
correspondence, the $\tau_J$-deformations are related to the insertions of
commuting integrals of motion in the four-point CFT correlator and chiral
correlators are expressed as $\tau$-derivatives of the gauge theory partition
function on a finite $\Omega$-background. In the so called Nekrasov-Shatashvili
limit, the entire ring of chiral relations is extracted from the
$\epsilon$-deformed Seiberg-Witten curve. As a byproduct of our analysis we
show that $SU(2)$ gauge theories on rational $\Omega$-backgrounds are dual to
CFT minimal models.
