A methodology is introduced for the identification of a multi-modal real-valued random variable from a collection of samples. The random variable is seen as a finite mixture of uni-modal random variables. A functional representation of the random variable is used, which can be interpreted as a {mixture of polynomial chaos expansions}. After a suitable separation of samples into sets of uni-modal samples, the coefficients of the expansion are identified by using an empirical projection technique. This identification procedure allows for a generic representation of a large class of multi-modal random variables with low-order generalized polynomial chaos representations.