  We consider multiple orthogonal polynomials associated with the exponential
cubic weight e^{-x^3} over two contours in the complex plane. We study the
basic properties of these polynomials, including the Rodrigues formula and
nearest-neighbor recurrence relations. It turns out that the recurrence
coefficients are related to a discrete Painlev\'e equation. The asymptotics of
the recurrence coefficients, the ratio of the diagonal multiple orthogonal
polynomials and the (scaled) zeros of these polynomials are also investigated.
