  We introduce lecture hall tableaux, which are fillings of a skew Young
diagram satisfying certain conditions. Lecture hall tableaux generalize both
lecture hall partitions and anti-lecture hall compositions, and also contain
reverse semistandard Young tableaux as a limit case. We show that the
coefficients in the Schur expansion of multivariate little $q$-Jacobi
polynomials are generating functions for lecture hall tableaux. Using a
Selberg-type integral we show that moments of multivariate little $q$-Jacobi
polynomials, which are equal to generating functions for lecture hall tableaux
of a Young diagram, have a product formula. We also explore various
combinatorial properties of lecture hall tableaux.
