  We consider a L\'evy driven continuous time moving average process $X$
sampled at random times which follow a renewal structure independent of $X$.
Asymptotic normality of the sample mean, the sample autocovariance, and the
sample autocorrelation is established under certain conditions on the kernel
and the random times. We compare our results to a classical non-random
equidistant sampling method and give an application to parameter estimation of
the L\'evy driven Ornstein-Uhlenbeck process.
