We have converted an ultracold Fermi gas of Li6 atoms into an ultracold gas of Li26 molecules by adiabatic passage through a Feshbach resonance. Approximately 1.5×105 molecules in the least-bound, v=38, vibrational level of the X1Σ+g singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.