We study n -quark systems ( n = 3, 6, 12) in the chiral bag model. In order to handle the non-linearities of the model, the hedgehog ansatz for the Goldstone pion field is used. It is found that due to “warping” of the quark orbits in the presence of mean-field pion clouds, a strong repulsion is developed when more than three quarks are put in a bag. This repulsion mechanism turns out to be close to the soliton mechanism discovered by Skyrme two decades ago. Even the magnitude of the repulsion agrees with his. It is also possible to relate the repulsion to the effective quenching of the axial charge of the multiquark system and a suggestion is made that the recently observed quenching of Gamow-Teller strengths in nuclei be interpreted in terms of the chiral structure of nuclear matter. Carrying over Skyrme's remarkable idea, we describe our baryon bag surrounded by the pion cloud as a chiral soliton. This part is quite tentative and many questions are left unanswered.