The phase-ordering kinetics for the growth of the ordered cholesteric liquid crystalline phase from the disordered isotropic melt is investigated at isothermal conditions after a temperature quench. The growth of a characteristic length, here the nucleus diameter, follows a universal growth law L(t) approximate to t(n) with the growth exponent changing from n = 1/2 in the vicinity of the transition to n = 1 for large quench depths. The short-term nucleus growth process is found to be dependent on the sample confinement with increasing growth exponents as the cell gap is increased. Nevertheless, no crossover from three-dimensional to two-dimensional growth could be observed as the nucleus diameter reached the dimension of the cell gap. a long-term coarsening process was found to be independent of the quench depth and confinement dimension, obeying a square-root growth law L(t) approximate to t(1/2).