This study is about one of the most ubiquitous and yet little studied aspects of ancient Greek religion, the offering of so-called ‘first-fruits’ (aparchai) and tithes (dekatai) in Archaic and Classical Greece (c.700-300 B.C.). A widespread and traditional custom all over Greece and the Greek Mediterranean, the offering of ‘first-fruits’ and tithes entailed using a portion of the proceeds from a diversity of human activities (such as craft-work, fishing, trade, military expeditions) to present something to the gods. I look at the different kinds of aparchai and dekatai offered to the Greek gods by individuals and states under various circumstances, the various contexts in which the language and practice of making such offerings were used, the deployment of this religious custom in politics, and the transformation of a voluntary practice into a religious obligation. Ultimately, however, my major concern is with questions of religious psychology: why people should bring aparchai and dekatai to the gods, and what motivations and expectations they might have had. Because it was such a commonplace practice, the custom has been taken simply as a given in both ancient and modern scholarship; and no attempt has been made to explain its religious significance. By drawing on current anthropological studies of gift-giving, I argue that that aparchai and dekatai do not merely give to the gods, but give back to the gods some of the benefits granted by the divinities in the first place, reflecting first and foremost a sense of dependence on the divine. I suggest that the offering of aparchai and dekatai may be thought of as a means of settling men’s debts to, and thereby maintaining good relations with, the gods, who were considered the sources of both goods and evils. I challenge the emphasis, common in modern scholarship, on material returns as the central motive behind the act of bringing gifts to the gods. Instead I suggest that the study of gift-giving between humans and the divine should embrace the possibility that psychological feelings of dependence on and gratitude to the gods might also have been involved.