  We prove a generalisation of Bollob\'as' classical result on the asymptotics
of the chromatic number of the binomial random graph to the stochastic block
model. In addition, by allowing the number of blocks to grow, we determine the
chromatic number in the Chung-Lu model. Our approach is based on the estimates
for the weighted independence number, where weights are specifically designed
to encapsulate inhomogeneities of the random graph.
