Stichomythia is a technique in drama or poetry, in which alternating lines, or half-lines, are given to alternating characters, voices, or entities. The term originated in the literature of Ancient Greece, and is often applied to the dramas of Sophocles, though others like Shakespeare are known to use it. Etymologically it derives from the Greek stichos ("rows") + mythos ("speech").
Stichomythia is particularly well suited to sections of dramatic dialogue where two characters are in violent dispute. The rhythmic intensity of the alternating lines combined with quick, biting ripostes in the dialogue can be quite powerful.
Example
A short example from the R.C. Jebb translation of Antigone:
ISMENE: And what life is dear to me, bereft of thee?
ANTIGONE: Ask Creon; all thy care is for him.
ISMENE: Why vex me thus, when it avails thee nought?
ANTIGONE: Indeed, if I mock, 'tis with pain that I mock thee.
ISMENE: Tell me,-how can I serve thee, even now?
ANTIGONE: Save thyself: I grudge not thy escape.
ISMENE: Ah, woe is me! And shall I have no share in thy fate?
ANTIGONE: Thy choice was to live; mine, to die.
ISMENE: At least thy choice was not made without my protest.
ANTIGONE: One world approved thy wisdom; another, mine.