To begin your essay, you can provide a brief introduction to Chance's character by describing his temperament, his relationship with women, and his outlook on life. For example, Chance is a gigolo, and he makes his living by having affairs with wealthy, older women. He is an opportunist who blatantly uses the aging but self-absorbed actress, Alexandra del Lago (Princess), to fulfill his own aims in life. In the play, Chance loves Heavenly, but her father, Boss Finley, stands in the way of their relationship. He will never consent to his daughter sullying her pedigree by marrying a drifter.
In order to illustrate how the character of Chance is developed through theatrical imagery, we can discuss:
1)The mythical legend of Adonis or Tammuz.
Chance is an Adonis figure, seemingly torn between two women, Heavenly and Princess. His mythical counterpart, Adonis, was so beautiful that the Goddess of Love, Aphrodite, and the Goddess of Death, Persephone, fought to keep him away from each other. In the end, Zeus decreed that Adonis must spend part of the year with Persephone (during winter) and another part of the year with Aphrodite (during spring and summer).
Another myth tells the story differently. In this story, Adonis' love of the woods and of hunting leads to his death. The god, Ares, jealous of Adonis' beauty, changes himself into a bull that gores Adonis to death while he hunts in the forest. To all intents and purposes, Ares castrates Adonis. To commemorate his death, yearly ceremonial plantings of 'Adonis gardens' continue the Adonis legend. Women would wail in lamentation for Adonis for seven days before he is 'reborn' through extensive ceremonies and elaborate celebrations. In the meantime, images of both Adonis and Aphrodite would be displayed on two couches as the lamentations continue.
In the play, certain imagery can be seen to develop this idea of Chance as an Adonis. First, we have the royal palm trees at the fashionable St. Cloud hotel where Chance and Princess are staying. This represents Adonis' sacred grove. The great double bed Chance and Alexandra sleep on suggests the bed of lamentation where Adonis and Aphrodite's images are displayed. In fact, throughout the play, auditory imagery in the form of a 'Lament' can be heard in the background. In the play, the bed also symbolizes the setting where the loss of sexual potency and the loss of youth are experienced. Both Chance and Alexandra cannot turn back the clock of time and are helpless to prevent Chance's implied castration at the end of the play.
Sources: The Rituals of Adonis.
Sweet Bird of Youth Analysis by Enotes.
Peter L. Hay's Use of Myth in Sweet Bird of Youth, Educational Theatre Journal
Vol. 18, No. 3, Special American Theater Issue (Oct., 1966), pp. 255-258
2)Imagery of the clock, birds, and the surgeon's knife.
Clocks often symbolize the passing of time. The clock imagery towards the end of the play may signify that time is up for Chance and that he has to redeem his past errors by submitting to the judgment of castration; as the surgeon's knife takes away Heavenly's ability to bear children, Chance must likewise be purified of his sins. Birds in flight often symbolize a need to escape and to free one's trapped desires. Towards the end of the play, birds in flight highlight Chance's predicament: he can run, but he can't hide from Boss Finley and his goons. Also, his youth and all the hopes of his early years are now beyond his grasp; every time he tries to reach for them, they fly beyond his vision and his presence.
The clock also symbolizes the fact that time stops for no man. However, Chance's philosophy is to race against time.
In a life like mine, you just can't stop, you know, can't take time out between steps, you've got to keep going right on up from one thing to the other, once you drop out, it leaves you and goes on without you and you're washed up.
For more on how theatrical imagery is used to develop Chance's character, you might be interested in the following link:
Elia Kazan and the Sweet Bird of Youth
Hope this helps!