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The crystal structure of synthetic kosmochlor, NaCr[Si.sub.2][O.sub.6], 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 [V.sub.0] = 418.84(3) [Angstrom]3, [K.sub.0] = 134(1) [GPa.sup.-1], and [K'.sub.0] = 2.0(3). Anisotropic compression was observed with unit strain axial ratios of 1:1.82:2.08. The Cr[O.sub.6] octahedron has a bulk modulus [K.sub.0] = 90(16) [GPa.sub.-1], while the Si[O.sub.4] tetrahedron has [K.sub.0] = 313(55) [GPa.sup.-1], both with [K'.sub.0] [equivalent to] 4. An o-type rotation of the O3-O3-O3 linkage was observed with pressure, with [angle] O3-O3-O3 decreasing from 172.8(2)[degrees] to 166.1(7)[degrees]. 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 [P2.sub.1]/c), LiSc[Si.sub.2][O.sub.6] (C2/c and [P2.sub.1]/c), clinoenstatite, orthoenstatite, and [Mg.sub.1.54] [Li.sub..23][Sc.sub..23][Si.sub.2][O.sub.6] (Pbcn and [P2.sub.1]cn) 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.