Chryseis was daughter to Chryses, himself a priest to Apollo. When Iliad opens, Chryses goes before the Greeks, in the interest of ransoming his daughter, who had been taken as a captive by Agamemnon, but Agamemnon refuses to release her. In so doing, Agamemnon invites the wrath of Apollo, outraged by this slight against his priest.
Beset by plague, the Greeks confer with Calchas, a prophet. Recognizing that his message would anger Agamemnon, he gets an oath from Achilles to defend him, and then proceeds to tell them the cause of Apollo's anger, revealing that the only recourse which the god might accept is to release Chryseis without any ransom at all. This message does outrage Agamemnon, striking at his pride (he resists giving up any part of his spoils) and in the process, he is brought into dispute with Achilles. This dispute will escalate when Agamemnon determines that, if he must return Chryseis, then he will recompense himself by taking Achilles's own war captive, Briseis. Thus Achilles and Agamemnon are in enmity.