Chemically and mechanically exfoliated MoS2 single-layer samples have substantially different properties. While mechanically exfoliated single-layers are monophase(1H polytype with Mo in trigonal prismatic coordination), the chemically exfoliated samples show coexistence of three different phases, 1H, 1T (Mo in octahedral coordination), and 1T' (a distorted 2 x 1 1T superstructure). By using first-principles calculations, we investigate the energetics and the dynamical stability of the three phases. We show that the 1H phase is the most stable one, while the metallic 1T phase, strongly unstable, undergoes a phase transition towards a metastable and insulating 1T' structure composed of separated zigzag chains. We calculate electronic structure, phonon dispersion, Raman frequencies, and intensities for the 1T' structure. We provide a microscopical description of the J(1), J(2), and J(3) Raman features that were first detected more than 20 years ago but have remained unexplained up to now. Finally, we show that H adsorbates, which are naturally present at the end of the chemical exfoliation process, stabilize the 1T' over the 1H one.