The chiral helimagnet Cr1/3NbS2 has been investigated by magnetic, transport and thermal properties measurements on single crystals and by first principles electronic structure calculations. From the measured field and temperature dependence of the magnetization for fields applied perpendicular to the c axis, the magnetic phase diagram has been constructed in the vicinity of the phase transitions. A transition from a paramagnetic to a magnetically ordered phase occurs near 120 K. With increasing magnetic field and at temperatures below 120 K, this material undergoes transitions from a helimagnetic to a soliton-lattice phase near 900 Oe, and then to a ferromagnetic phase near 1300 Oe. The transitions are found to strongly affect the electrical transport. The resistivity decreases sharply upon cooling near 120 K, and the spin reorientation from the helimagnetic ground state to the commensurate ferromagnetic state is evident in the magnetoresistance. At high fields a large magnetoresistance (55 % at 140 kOe) is observed near the magnetic transition temperature. Heat capacity and electronic structure calculations show the density of states at the Fermi level is low in the magnetically ordered state. Effects of spin fluctuations are likely important in understanding the behavior of Cr1/3NbS2 near and above the magnetic ordering transitions.