The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS3 on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T-0 approximate to 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B parallel to C) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T-0. The negative magnetoresistance (at B parallel to c) below T-0 is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B parallel to ab) is explained by the effect of the magnetic field on the spectrum of electronic states.