A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu ≠ 1 for u = 1,…, N, and quaternions s1,…, sN, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.