We report the first 3D spin liquid state of isotropic organic spins. Structural analysis, and magnetic and heat-capacity measurements were carried out for a chiral organic radical salt, (TBA)_{1.5}[(-)-NDI-Δ] (TBA denotes tetrabutylammonium and NDI denotes naphthalene diimide), in which (-)-NDI-Δ forms a K_{4} structure due to its triangular molecular structure and an intermolecular π-π overlap between the NDI moieties. This lattice was identical to the hyperkagome lattice of S=1/2 Mott dimers, and should exhibit 3D spin frustration. In fact, even though the high-temperature magnetic susceptibility followed the Curie-Weiss law with a negative Weiss constant of θ=-15 K, the low-temperature magnetic measurements revealed no long-range magnetic ordering down to 70 mK, and suggested the presence of a spin liquid state with a large residual paramagnetism χ_{0} of 8.5×10^{-6} emu g^{-1} at the absolute zero temperature. This was supported by the ^{14}N NMR measurements down to 0.38 K. Further, the low-temperature heat capacities c_{p} down to 68 mK clearly indicated the presence of c_{p} for the spin liquid state, which can be fitted to the power law of T^{0.62} in the wide temperature range 0.07-4.5 K.