The recent observation that constituent quark helicities carry very little of the spin of the proton, in contrast with naive quark model expectations, can be understood by taking into account non-perturbative aspects of QCD, such as chiral symmetry breaking and confinement. We compute the non-strange quark contribution ∆u+∆d to the proton spin in a chiral field-theoretical model of quark and gluon confinement. Our mean field computations include self-consistently the effects of gluon exchange between constituent quarks. When the parameters of the model, including the effective strong fine structure constant αs, are adjusted to reproduce as far as possible the experimental mean nucleon-delta mass and the relative nucleon-delta mass splitting, we obtain ∆u+∆d⋍0.26, which is only one third of the αs=0 value. We show that this implies that all the proton spin is in fact orbital angular momentum.