  Using non-Archimedian integration over spaces of arcs of algebraic varieties,
we define stringy Euler numbers associated with arbitrary Kawamata log terminal
pairs. There is a natural Kawamata log terminal pair corresponding to an
algebraic variety V having a regular action of a finite group G. In this
situation we show that the stringy Euler number of this pair coincides with the
physicists' orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten
formula. As an application, we prove a conjecture of Miles Reid on the Euler
numbers of crepant desingularizations of Gorenstein quotient singularities.
