The phase diagram of BaVS3 is studied under pressure using resistivity meas
urements. The temperature of the metal to nonmagnetic Mott insulator transi
tion decreases under pressure, and vanishes at the quantum critical point p
(cr) = 20 kbar. We find two kinds of anomalous conducting states. The high-
pressure metallic phase is a non-Fermi liquid described by Delta rho propor
tional to T-n where n = 1.2-1.3 at 1 < T < 40 K. At p < p(cr), the transiti
on is preceded by a wide precursor region with critically increasing resist
ivity which we ascribe to the opening of a soft Coulomb gap.