We analyze the two-nucleon system below the pion threshold, using a chiral quark cluster model. We solve multichannel resonating group method equations in momentum space, treating them as a set of Lippmann-Schwinger equations. Deuteron data and scattering phase shifts up to a total angular momentum J= 6 are presented. Full couplings to N Δ and Δ Δ channels are considered and analyzed. High angular momentum partial waves (L> 2) provide a detailed test of chiral symmetry in the two-nucleon system. D waves still show important short-range effects. Low angular momentum partial waves and deuteron observables are in good agreement with the experimental data, showing that the underlying quark structure provides the required short-range potential behavior.