We present a Skyrme model with modified kinetic-energy terms. The baryon current of the model supports both fractional and integer baryon number solutions. Chiral symmetry breaking renders the fractional baryon number states absolutely confined. In the unbroken phase the solutions bear resemblance to the constitutent quarks of the nonrelativistic quark model. The model predicts correctly the nucleon and delta resonance masses using a value for the pion decay constant [ital F][sub [pi]] very close to experiment. The model yields an attractive central potential between nucleons.