We have identified a three-dimensional spin texture in the two-dimensional electron gas (2DEG) at the SrTiO3 (111) surface. In a free-electron Rashba 2DEG system the induced spin polarization lies entirely in the plane of confinement. Our tight binding supercell calculations for the SrTiO3 (111) 2DEG reveal a Rashba spin-splitting with a significant out-of-plane component in addition to the expected in-plane component with spin-momentum locking. The spin-component perpendicular to the confinement plane has only three-fold rotational symmetry. This results in a clear three-fold symmetric signal in second harmonic magneto-resistance measurements of Ar+ irradiated SrTiO3 (111) 2DEGs, thereby providing experimental evidence for this 3D spin texture. The out-of-plane spin component we observe is a manifestation of the strong crystal field of bulk SrTiO3 which imposes a preferential spin direction along the <001> axis. In the case of the (111) surface 2DEG, this preferential direction does not lie in the plane of confinement and thus the electron spins naturally carry an out-of plane component. Our work is accepted for publication in Physical Review Letters and can be found on the cond-mat arXiv.