Ajax, a Greek commander, bids Thersites, an old, bitter man and Ajax's servant, to find out the contents of a proclamation but no avail. Theristes calls Ajax a clumsy fool for which he is beaten by Ajax. Their commotion attracts other Greek commanders: namely, Achilles and Patroclus. Achilles acts as the arbiter, preventing Ajax from continuously beating Thersites and making it clear to Thersites that he does not share the same privileges accorded Ajax as he--Thersites--is a conscripted man. Spiteful as ever, Thersites takes his leave, cursing the whole lot of them and arguing that Hector will get the better of any one of them on the battlefield. Presently, Achilles informs Ajax that the proclamation has to do with Hector’s challenge to engage a nobleman of Greece in one-on-one combat. Ajax goes to find out if Hector’s challenge applies specifically to Achilles and only Achilles as Ajax suspects it is, or if it is, as Achilles claims, a challenge that any Greek noble might answer.
As Nestor, a Greek commander, has clarified the position of the Greeks, that the Greeks are willing to withdraw from Troy and let bygones be bygones if Troy will only return Helen to her rightful place, i.e. besides Menelaus, Priam confers with his sons as to what they should do. Hector counsels that they should return Helen, arguing that the cost of keeping Helen exceeds her intrinsic value. Troilus argues, however, that Helen’s value is such that the Greeks have a launched a thousand ships to reclaim her. Should Troy have stolen from the Greeks something of less value, something that would not have brought upon their heads the wrath of the Greeks? Would that have been more honorable? Paris agrees with Troilus, arguing that there isn’t a Trojan alive who wouldn’t stake his life for Troy’s cause to keep Helen, that to give Helen up would be as good as admitting that Troy is too cowardly to stand by her convictions. Though likening Troilus and Paris to young men who reason with their hearts rather than their minds, Hector concedes that their argument has merit and resolves to be in one mind/heart with them. Hector mentions his challenge to the Greeks and his eagerness to engage whoever answers it.
Bitter that he had been beaten by Ajax, Thersites belittles the Greeks for waging war for the sake of a woman. By and by, he finds himself in the company of Achilles and Patroclus who are both eager to engage him. Thersites claims that all of them, including Agamemnon, Achilles, Thersites himself, and especially Patroclus are fools, an opinion Patroclus objects to but which Achilles abides, reminding Patroclus that Thersites is an all-licensed fool (and therefore allowed to say just about anything). Presently, espying the approach of Agamemnon and his attendants, Achilles goes into his tent where he will ensconce himself to avoid and slight Agamemnon on purpose. As to Patroclus, he is told to keep the approaching company from entering Achilles’ tent. Patroclus does as he is bid, stating that Achilles has come down with an illness and therefore will not receive any visitors. Agamemnon tells Patroclus to tell Achilles that he--Agamemnon--has come in person as Achilles has ignored all of Agamemnon’s messengers. As Patroclus goes in to do so, Ulysses and Nestor talk, revealing their plan to keep Achilles and Ajax at odds. Patroclus returns to say that Achilles is sorry that Agamemnon has come out as far as he has and will only assume that he has done so for digestion purposes. Annoyed, Agamemnon has Patroclus deliver the message that Agamemnon knows Achilles, driven by his pride, is avoiding Agamemnon on purpose and that it behooves Achilles to show some respect lest his pride besmirch his well-earned achievements and reputation. Patroclus goes in followed by Ulysses who is sent in to get the lowdown.
Ulysses returns to say that Achilles will not answer Hector’s challenge, that he is too proud to relent to Agamemnon’s will. Agamemnon thinks about sending in Ajax to talk to Achilles but he is dissuaded from doing so by Ulysses who argues that Ajax is as good a man as Achilles and does not deserve to be treated as Achilles’ lackey. By and by, Nestor, Diomedes, and even Agamemnon join Ulysses in singing Ajax’s praises, while really disparaging Ajax with remarks off to the side, so that Ajax believes that he is indeed a warrior who is equal to, if not a warrior better than, Achilles.