Within density functional theory we study the bulk band structure and surface states of bismuth oxychalcogenides Bi2O2Se and Bi2O2Te. We consider both polar and nonpolar surface terminations. On the basis of relativistic ab initio calculations, we show that both unreconstructed (polar) and reconstructed (nonpolar) surfaces possess the Rashba spin-split surface states. The metallic Rashba-split states on polar surfaces stem from huge potential bending, positive or negative, depending on surface polarity. On the nonpolar surfaces resulting from single-crystal cleavage the emerging Rashba-split states are nonmetallic.