Recently, we reported STM images of the methylated Si(111) surface [prepared through chlorination-alkylation of the Si(111)-H surface] taken at 4.7 K, indicating that the torsion angle of the methyl group with respect to the subsurface silicon layer is phi = 23 +/- 3 degrees . Repulsions between H atoms in adjacent methyl groups are minimized at 30 degrees , while repulsions between H atoms and second layer Si atoms are minimized at 60 degrees . The experimental result of 23 degrees is surprising because it suggests a tendency of the methyl group toward the eclipsed configuration (0 degrees ) rather than staggered (60 degrees ). In contrast, extensive fully periodic quantum mechanical Density Functional Theory studies of this surface give an equilibrium torsion angle of 37.5 degrees , indicating a tendency toward the staggered configuration. This discrepancy can be resolved by showing that the CH3 on the step edges and etch pits interacts repulsively with the CH3 on the surface terraces unless a stacking fault is introduced between the first and second silicon layers of the Si(111)-CH3 surface terraces. We propose that this could occur during the chlorination-alkylation of the Si(111)-H surface. This stacking fault model predicted phi = 22.5 degrees measured with respect to the bulk (corresponding to phi = 37.5 degrees with respect to the second layer Si atoms). This model can be tested by measuring the orientation of the CH3 within the etch pits, which should have phi = 37.5 degrees , or by making a surface without etch pits, which should have phi = 37.5 degrees .