We present a method for the preparation of GaAs-AlGaAs quantum wire arrays starting from holographically prepared masks. The combination of reactive ion etching and stepwise wet-chemical etching allows us to produce narrow quantum wires. We achieved wire widths down to 40 nm. The diamagnetic shift of the magnetoexcitons in our samples shows clear evidence of enhanced Coulomb interaction between photocreated electrons and holes due to the lateral confinement. A decrease of the lateral extension of the excitonic wave function from 10.6 nm in the 2D reference sample to 7.4 nm in the 40 nm wide quantum wires is deduced from the data.