The chiral quark-meson model based on a linear σ-model is extended to three flavours of quarks. We describe the choice of parameters and the features of the hedgehog solitons both in the SU(3)-symmetric limit and with realistic symmetry breaking. For the case of unbroken symmetry the approximate projection method of Birse and Banerjee is used to calculate properties of the octet baryons. The magnetic moments are found to be in reasonable agreement with experiment, with most of the discrepancy being accounted for by the fact that the kaons and pions are degenerate. Lowest-order cranking is used to calculate the mass splittings between the baryon multiplets. The isospin cranking which governs the octet-decuplet splitting is very similar to that in the SU(2) model. The moment of inertia for "strange" rotations gives the energies of states which must involve mesonic excitations. It is found to be small, indicating that such states, if they exist, lie well above the nucleon.