The goal of the FAST experiment is the precise measurement of the muon lifetime, to the accuracy of 2 ppm. After including the theoretical and experimental errors, this results in a precise measurement of the Fermi coupling constant, to a precision that is one order of magnitude better than the present world average. FAST consists in a high granularity scintillator target, where a positive pion beam (from PSI accelerator facility) is stopped. The pions decay at rest inside the target; the consequent decays of muons into positrons are registered by the readout chain. The times of the particles are measured, and the muon lifetime is extracted. The high precision requirement imposes a high statistics collection of muon decay events (order of a few 10¹¹ events). This work presents the first measurement of the muon lifetime with FAST, with the analysis of a data sample of ~10¹° muon decay events, collected in December 2006. The precision of the measurement (16 ppm) is competitive with the world average.