The influence of the quenched randomness in the stereochemical sequences of atactic chains on the mean-square unperturbed end-to-end distance, < r(2)>(0), is assessed. The method uses a rotational isomeric state (RIS) model based on virtual bonds between the centers of mass of the C-6 rings in polystyrene. This virtual bond model is derived from a conventional RIS model expressed in terms of the C-C bonds in the main chain. The zeroth-approximation virtual bond model, which retains only the most probable conformations of each tetrad, correctly finds < r(2)>(0) similar to n in the limit as n -> infinity if the probability for a meso diad, pm, is 0 < p(m) < 1, although the same zeroth-approximation model yields < r(2)>(0) similar to n(2) if p(m) is either 0 or 1. The values of < r(2)>(0) at intermediate p(m) are surprisingly close to the ones deduced from a full, C-C bond based RIS model. This achievement of the zeroth-approximation model demonstrates the important role of the quenched randomness of the stereochemical sequences in determining the unperturbed dimensions of atactic chains. Excellent agreement with the < r(2)>(0) from the full RIS model based on C-C bonds over the entire range of stereochemical composition, 0 <= p(m) <= 1, can be achieved in a first-approximation virtual bond model, which includes the next most probable conformations at each tetrad and refines slightly some of the conformations by minor adjustments in soft degrees of freedom.