Strain glass transition is a unique nanoscale displacive transition with local symmetry breaking while maintaining the macroscopic symmetry or average structure unchanged. It usually occurs in the "nonmartensitic" composition range of a martensitic system. So far, only indirect evidence exists for such a transition, essentially from macroscopic measurements and low-resolution transmission electron microscopy observations, and there is a lack of direct evidence for the speculated local symmetry breaking and the sluggish nature of the glass transition. In this Letter we report in situ high-resolution transmission electron microscopy observations on a Ti50(Pd41Cr9) strain glass alloy and direct evidence for these key issues. Our results show that at temperatures well above the strain glass transition temperature (Tg), the lattice is essentially an undistorted B2 structure. With approaching Tg, the local symmetry breaking gradually occurs with the formation and growth of nanomartensite clusters with a combined stacking period of three and four plane intervals, but the average structure measured by x-ray diffraction remains B2. These nanomartensite clusters become finally frozen below Tg. Our results provide not only a microscopic basis for the macroscopic properties of strain glass, but also new insights into a range of possible applications of this unique class of materials.