The aim of the MuCap experiment is a 1% measurement of the singlet capture rate Lambda_S for the basic electro-weak reaction mu + p -> n + nu_mu. This observable is sensitive to the weak form-factors of the nucleon, in particular to the induced pseudoscalar coupling constant g_P. It will provide a rigorous test of theoretical predictions based on the Standard Model and effective theories of QCD. The present method is based on high precision lifetime measurements of mu^- in hydrogen gas and the comparison with the free mu^+ lifetime. The mu^- experiment will be performed in ultra-clean, deuterium-depleted H_2 gas at 10 bar. Low density compared to liquid H_2 is chosen to avoid uncertainties due to ppmu formation. A time projection chamber acts as a pure hydrogen active target. It defines the muon stop position in 3-D and detects rare background reactions. Decay electrons are tracked in cylindrical wire-chambers and a scintillator array covering 75% of 4 pi.