NGC1275 is the Brightest Cluster Galaxy (BCG) in the Perseus cluster and hosts the active galactic nucleus (AGN) that is heating the central 100,kpc of the intracluster medium (ICM) atmosphere via a regulated feedback loop. Here we use a deep 490ks Cycle-19 Chandra High-Energy Transmission Grating (HETG) observation of NGC1275 to study the anatomy of this AGN. The X-ray continuum is adequately described by an unabsorbed power-law with photon index $Gammaapprox 1.9$, creating strong tension with the detected column of molecular gas seen via HCN and HCO$^+$ line absorption against the parsec-scale core/jet. This tension is resolved if we permit a composite X-ray source; allowing a column of $N_Hsim 8times 10^{22},{rm cm}^{-2}$ to cover $sim 15$% of the X-ray emitter does produce a significant improvement in the statistical quality of the spectral fit. We suggest that the dominant unabsorbed component corresponds to the accretion disk corona, and the sub-dominant X-ray component is the jet working surface and/or jet cocoon that is expanding into clumpy molecular gas. We suggest that this may be a common occurence in BCG-AGN. We conduct a search for photoionized absorbers/winds and fail to detect such a component, ruling out columns and ionization parameters often seen in many other Seyfert galaxies. We detect the 6.4keV iron-K$alpha$ fluorescence line seen previously by XMM-Newton and Hitomi. We describe an analysis methodology which combines dispersive HETG spectra, non-dispersive microcalorimeter spectra, and sensitive XMM-Newton/EPIC spectra in order to constrain (sub)arcsec-scale extensions of the iron-K$alpha$ emission region.
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