The crystal structure of synthetic kosmochlor, NaCrSi2O6, was studied using single crystal X-ray diffraction at high pressure. A four-pin diamond anvil cell, with 4:1 methanol:ethanol pressure medium, was used to achieve pressures to 9.28 GPa. Unit-cell data were collected at 20 pressures, and intensity data were collected at 13 of these pressures. Fitting the P-V data to a third-order Birch-Murnaghan equation yields V0 = 418.84(3) Å3, K0 = 134(1) GPa−1, and K0′ = 2.0(3). Anisotropic compression was observed with unit strain axial ratios of 1:1.82:2.08. The CrO6 octahedron has a bulk modulus K0 = 90(16) GPa−1, while the SiO4 tetrahedron has K0 = 313(55) GPa−1, both with K0 ′ ≡4. An o-type rotation of the O3-O3-O3 linkage was observed with pressure, with ∠O3-O3-O3 decreasing from 172.8(2)° to 166.1(7) °. Compression in kosmochlor is related to the stacking directions of distorted cubic closest packed O atom monolayers. Unit strain ellipsoids for diopside, hedenbergite, spodumene (C2/c and P21/c), LiScSi2O6 (C2/c and P21/c), clinoenstatite, orthoenstatite, and Mg1.54Li.23Sc.23Si2O6 (Pbcn and P21cn) were generated and discussed in terms of closest packing systematics. A relationship between the anisotropy of compression of olivines and pyroxenes is established. A strategy to determine not only the direction of a stress field in deformed rocks, but also an estimate of the magnitude of stress is discussed in terms of comparing the anisotropy of olivine and pyroxene.