We report the observation of stacking fault tetrahedra (SFT) in strained Si1-xGex layers grown via rapid thermal CVD on (111) Si substrates. It is shown that these defects provide a mechanism for strain relief in films strained in compression due the presence of bounding edge-type stair rod partials whose Burgers vectors lie parallel to the strained layer interface. Cross section and plan view TEM were used to characterize this defect structure in epilayers (30 to 650nm thick) of Si1-xGex (0 < xGe < 0.27) grown on 〈111〉 oriented Si wafers. Stacking fault tetrahedra were observed only in alloys in the compositional range xGe ≥ 0.13 and only when growth proceeded on the 〈111〉 surface. A critical strain energy model that identifies conditions for the stable growth of stacking fault tetrahedra in a strained layer is presented. The model was based on conventional strain energy considerations where the energy of the stacking fault area plus the bounding dislocation network (including dislocation interactions but neglecting the free surface) was balanced against the strain energy released by the introduction of the defect. In addition, a formation mechanism consistent with these observations is described that involves the dissociation of Frank partial dislocation loops bounding stacking faults lying in the growth plane.