We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis–Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.