Nanocrystalline materials offer very high strength but are typically limited in their strain to failure, and efforts to improve deformability in these materials are usually found to be at the expense of strength. Using a combination of quantitative in situ compression in a transmission electron microscope and finite-element analysis, we show that the mechanical properties of nanoparticles can be directly measured and interpreted on an individual basis. We find that nanocrystalline CdS synthesized into a spherical shell geometry is capable of withstanding extreme stresses (approaching the ideal shear strength of CdS). This unusual strength enables the spherical shells to exhibit considerable deformation to failure (up to 20% of the sphere's diameter). By taking into account the structural hierarchy intrinsic to novel nanocrystalline materials such as this, we show it is possible to achieve and characterize the ultrahigh stresses and strains that exist within a single nanoparticle during deformation.