The charge radius of the proton, the simplest nucleus, is known from electron-scattering experiments only with a surprisingly low precision of about 2%. The poor knowledge of the proton charge radius restricts tests of bound-state quantum electrodynamics (QED) to the precision level of about 6 × 10^–6, although the experimental data themselves (1S Lamb shift in hydrogen) have reached a precision of 2 × 10^–6. The determination of the proton charge radius with an accuracy of 10^–3 is the main goal of our experiment, opening a way to check bound-state QED predictions to a level of 10^–7. The principle is to measure the 2S–2P energy difference in muonic hydrogen (µ^–p) by infrared laser spectroscopy. The first data were taken in the second half of 2003. Muons from our unique very-low-energy muon beam are stopped at a rate of ~100 s^–1 in 0.6 mbar H₂ gas where the lifetime of the formed µp(2S) atoms is about 1.3 µs. An incoming muon triggers a pulsed multistage laser system that delivers ~0.2 mJ at λ ≈ 6 µm. Following the laser excitation µp(2S) → µp(2P) we observe the 1.9 keV X-rays from 2P–1S transitions using large area avalanche photodiodes. The resonance frequency, and, hence, the Lamb shift and the proton radius, is determined by measuring the intensity of these X-rays as a function of the laser wavelength. A broad range of laser frequencies was scanned in 2003 and the analysis is currently under way. PACS Nos.: 36.10.Dr, 14.20.Dh, 42.62.Fi