  What is the size of the most massive object one expects to find in a survey
of a given volume? In this paper, we present a solution to this problem using
Extreme-Value Statistics, taking into account primordial non-Gaussianity and
its effects on the abundance and the clustering of rare objects. We calculate
the probability density function (pdf) of extreme-mass clusters in a survey
volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We
also study the sensitivity of the extreme-value pdfs to changes in the mass
functions, survey volume, redshift coverage and the normalization of the matter
power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL,
our correction for the extreme-value pdf due to the bias is important when f_NL
> O(100), and becomes more significant for wider and deeper surveys. Applying
our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find
that its existence is consistent with f_NL = 0, although the conclusion is
sensitive to the assumed values of the survey area and {\sigma}_8. We also
discuss the convergence of the extreme-value distribution to one of the three
possible asymptotic forms, and argue that the convergence is insensitive to the
presence of non-Gaussianity.
