The rotational dynamics of cations and anions in the room temperature ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate ([C(4)mim]PF6) have been investigated in the supercooled liquid and glassy states using C-13, P-31, and F-19 NMR spectroscopy. The alpha-relaxation process of the supercooled liquid corresponds well with that of the isotropic rotational reorientation of the [C(4)mim](+) cations. The timescale of the reorientational motion of the butyl chain in the cations, which is reminiscent of the conformational isomerization, is found to be slower than that of the imidazolium ring. This counterintuitive result can be attributed to the presence of local structures in the form of polar and nonpolar nanodomains in the liquid and significant steric and coulombic interactions between the rings or chains in the cations and such domains. On the other hand, the dynamics of the constituent PF6- anions is dominated by free rotational diffusion at temperatures above similar to 230 K, while a restricted rotational or librational motion dominates at lower temperatures. This transition temperature can be identified with the mode coupling critical temperature T-c where the anion rotational timescale decouples from that of the [C(4)mim](+) cations. The librational motion of the anions has a characteristic timescale on the order of 10(-10) s with an activation energy of similar to 0.16 eV typical of a beta-relaxation process. This dynamical process continues below T-g, well into the glassy state of this ionic liquid.