We have obtained analytical expressions for the radiative decay rate of the spontaneous emission of a chiral molecule located near a dielectric spherical particle with a chiral nonconcentric spherical shell made of a bi-isotropic material. Our numerical and graphical analyses show that material composition, thickness and degree of non-concentricity of the shell can influence significantly the spontaneous radiation of the chiral molecule. In particular, the radiative decay rates can differ in orders of magnitude for a chiral molecule located near the thin and thick parts of a nonconcentric shell as well as near a concentric shell made of chiral metamaterial. We also find that the radiative decay rates of the "right" and "left" chiral molecule enantiomers located near a nanoparticle with a chiral metamaterial shell can differ pronouncedly from each other. Our findings therefore suggest a way to tune the spontaneous emission of chiral molecules by varying the material composition, thickness and degree of non-concentricity of the shell in the nearby composite nanoparticle and also to enhance the chirality selection of chiral molecules in racemic mixtures.