  Conditional independence (CI) testing arises naturally in many scientific
problems and applications domains. The goal of this problem is to investigate
the conditional independence between a response variable $Y$ and another
variable $X$, while controlling for the effect of a high-dimensional
confounding variable $Z$. In this paper, we introduce a novel test, called
`Pearson Chi-squared Conditional Randomization' (PCR) test, which uses the
distributional information on covariates $X,Z$ and constructs randomizations to
test conditional independence. Our proposal is motivated by some of the hard
alternatives for the vanilla conditional randomization test (Cand\`es et al.,
2018).
  We also provide a power analysis of the PCR test, which captures the effect
of various parameters of the test, the sample size and the distance of the
alternative from the set of null distributions, measured in terms of a notion
called `conditional relative density'. In addition, we propose two extensions
of the PCR test, with important practical implications: $(i)$ parameter-free
PCR, which uses Bonferroni's correction to decide on a tuning parameter in the
test; $(ii)$ robust PCR, which avoids inflations in the size of the test when
there is slight error in estimating the conditional law $P_{X|Z}$.
