The first direct observation of muonium (Mu) precession in a solid was achieved in 1988 using positive muons stopped in fused quartz (Si02) at 7.2 G. I Since then, fused Si02 has been routinely used to calibrate the efficiency of other materials for Nu formation, since the p+ Terms Mu with higher probability in Si02 than in any other solid known. 2 In the original experiment, I the apparent relaxation rate of the Nu polarization was seen to be faster in crystalline Si02 than in fused Si02, but no special significance was attached to this Tact. Fused quartz was also the first medium in which the PaschenBach effect was shown to produce "two-frequency precession" of Mu in magnetic fields ~ 50 G, ~ which has been used to measure the strength of the Fermi contact interaotien between ~+ and espins in the strongly-coupled "deep" Nu atom in Si02, Go, and Si. 2-~ This interaction is normally isotrepic, but in Si crystals a dramatic anisotropy has been observed in the phenomenological hyperfine interaction in a second, weakly-coupled, "shallow" Nu* state, s Crystalline quartz has spiral symmetry about a single ~ axis. In e perfect single crystal the spiral has e unique helieity so that the crystal is either D (right-handed) or L (left-handed). Natural crystals suffer from "twinning," i.e., they are composed of many regions of alternately O and L structure. However, artificially grown crystals can be made virtually free of twinning. The availability of such pure Dor L-quartz crystals motivated an experiment at TRIUMF to determine whether polarized positive muons stopped in Dand L-Si02 have different probabilities of capturing electrons with spins parallel to their own (reflected in the initial polarization of the resultant Mu atoms and thus in the amplitude of the subsequent triplet Mu precession). 6 Interest in such a possibility stems from recent experiments on pesitronium formation in B and L enantiomsrs of amino acids, where such a preference has been reported. Any effect o~ this sort would have implications for the theory of the origin of unique chirality in biological molecules. ~ Although it is possible to say at this time that the magnitude of any such effect on the amplitude of Mu precession in quartz crystals is less than a few percent, the current experiment (whose sensitivity should be on the order of I%) is not yet complete. 6 However, in the course of these studies a surprising and unrelated phenomenon was discovered: triplet Mu precession in quartz crystals was observed to be split into two clearly resolved frequencies separated by about 0.4 NHz in a magnetic field o~ 4.25 G, where the usual splitting due to the Paechen-Bach effect should be only 0.0079 MHz.