  We present a calculation of pseudoscalar Higgs production in association with
a jet at Next-to-Next-to Leading Order (NNLO) accuracy in QCD. We work in an
effective field theory in which $m_t \rightarrow \infty$ resulting in effective
operators which couple the pseudoscalar to gluons and (massless) quarks. We
have calculated all of the relevant amplitudes for the two-loop, one-loop and
tree-level contributions. As a cross-check of our calculation we have
re-calculated all of the scalar Higgs plus parton amplitudes and perform a
detailed comparison to the literature. In order to regulate the infra-red
singularities present at this order we employ the $N-$jettiness slicing method.
In addition to a detailed validation of our calculation at this order we
investigate LHC phenomenology for a selection of pseudoscalar Higgs masses. Our
results are implemented into the parton-level Monte Carlo code MCFM.
