We report new experimental and theoretical results on the problem of reaction-diffusion in a microfluidic chip. The chemical reactor under study is a T-shaped microchannel (about 200~$\mu$m wide and 10--20~$\mu$m deep) in which the two analytes are bring into contact at a constant flow rate. In the interdiffusion zone, the local concentration of the reaction product is measured using optical epi-fluorescence. To extract useful informations about the reaction kinetics, one needs to model the reaction-diffusion zone and compare the simulations with the experiments. We show that such a microfluidic device is a well-suited method to access fast chemical kinetic rates.