The spin-1/2 stacked triangular antiferromagnet CsCu$_{1-x}$Co$_x$Cl$_3$ with $0.015<x<0.032$ undergoes two phase transitions at zero field. The low-temperature phase is produced by the small amount of Co$^{2+}$ doping. In order to investigate the magnetic structures of the two ordered phases, the neutron elastic scattering experiments have been carried out for the sample with $xapprox 0.03$. It is found that the intermediate phase is identical to the ordered phase of CsCuCl$_3$, and that the low-temperature phase is an oblique triangular antiferromagnetic phase in which the spins form a triangular structure in a plane tilted from the basal plane. The tilting angle which is 42$^{circ}$ at $T=1.6$ K decreases with increasing temperature, and becomes zero at $T_{rm N2} =7.2$ K. An off-diagonal exchange term is proposed as the origin of the oblique phase.