  We study the number of isolated vertices in a preferential attachment random
graph introduced by Dereich and M\"orters in 2009. In this graph model vertices
are added over time and newly arriving vertices connect to older ones with
probability proportional to a (sub-)linear function of the indegree of the
older vertex at that time. Using Stein's method and a size-bias coupling, we
deduce bounds in the Wasserstein distance between the law of the properly
rescaled number of isolated vertices and a standard Gaussian distribution.
