  We present a heuristic derivation of Gaussian approximations for stochastic
chemical reaction systems with distributed delay. In particular we derive the
corresponding chemical Langevin equation. Due to the non-Markovian character of
the underlying dynamics these equations are integro-differential equations, and
the noise in the Gaussian approximation is coloured. Following on from the
chemical Langevin equation a further reduction leads to the linear-noise
approximation. We apply the formalism to a delay variant of the celebrated
Brusselator model, and show how it can be used to characterise noise-driven
quasi-cycles, as well as noise-triggered spiking. We find surprisingly
intricate dependence of the typical frequency of quasi-cycles on the delay
period.
