  We investigate a disordered variant of Pitman's Chinese restaurant process
where tables carry i.i.d. weights. Incoming customers choose to sit at an
occupied table with a probability proportional to the product of its occupancy
and its weight, or they sit at an unoccupied table with a probability
proportional to a parameter $\theta>0$. This is a system out of equilibrium
where the proportion of customers at any given table converges to zero almost
surely. We show that for weight distributions in any of the three extreme value
classes, Weibull, Gumbel or Fr\'echet, the proportion of customers sitting at
the largest table converges to one in probability, but not almost surely, and
the proportion of customers sitting at either of the largest two tables
converges to one almost surely.
