In this paper, the process of a drop rebounding from a hydrophobic and chemically heterogeneous surface is investigated using the multiphase lattice Boltzmann method. The bounce behavior of drops is dependent on the degree of hydrophobicity and heterogeneity of the surface. When the surface is homogeneous, the drop rebounds vertically and the height increases with the enhancement of the surface hydrophobicity. For the heterogeneous surface with two different hydrophobic parts, the drop rebounds laterally toward the lower hydrophobic side. Because the high hydrophobic side exerts the stronger unbalanced Young's force on the contact line compared with the low hydrophobic side, the difference of the forces results in the asymmetrical rebound. A phase diagram displays the rebound numbers of a drop impacting on the various chemically homogeneous and heterogeneous surfaces. A simply quantitative estimation is made to predict the rebound heights and flying times through the contact angles of the surface. This work promotes the understanding of the rebound mechanism of a drop impacting on a chemically heterogeneous surface and provides a guiding strategy for the precise control of the lateral behavior of rebounding drops by hydrophobic and heterogeneous surfaces.