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By means of variational methods and systematic numerical analysis, wedemonstrate the existence of stable solitons in three-dimensional (3D) freespace, in the context of binary atomic condensates combining contactself-attraction and spin-orbit coupling, which can be engineered by availableexperimental techniques. Depending on the relative strength of the intra- andinter-component attraction, the stable solitons feature a semi-vortex ormixed-mode structure. In spite of the fact that the local cubic self-attractiongives rise to the supercritical collapse in 3D, the solitons are stable againstrandom perturbations, motion, and collisions.

Stable Solitons in Three Dimensional Free Space: Self-Trapped Bose-Einstein Condensates with Spin-Orbit Coupling