An infrared-divergent interaction previously shown to lead to confinement in the quark-antiquark bound-state problem is used in the three-quark problem. Once again the divergent quark self-energy is canceled by the binding energy, leading to a finite Bethe-Salpeter bound-state equation, only in a color-singlet state. The key to the method is the decomposition of the bound-state amplitude into a sum of three terms, each of which depends on only one energy variable; analysis of the amplitude's pole structure then becomes possible. Confinement is demonstrated and ground-state energy is estimated variationally.