Cut grapefruit in half. With a curved grapefruit knife, cut around each section to loosen the flesh from the membrane; remove and reserve the sections of fruit. Squeeze the juice from the shells to equal 1/3 cup.
With a spoon, scrape the grapefruit shells clean. Scallop or notch the edges, if desired (*see note below). Chill.
While the shells are chilling, season chicken with salt and pepper to taste. Cook the chicken for about 10 minutes over moderate heat in a nonstick pan or until chicken is no longer pink.
Combine the reserved grapefruit sections, chicken, avocado and green onions in a bowl.
Combine the 1/3 cup reserved grapefruit juice with the other dressing ingredients. Pour over the chicken mixture; mix lightly. Cover and chill for 30 minutes.
To serve, use a slotted spoon to transfer the chicken mixture to the grapefruit shells, then top with as much dressing as desired.
*Note: To scallop any citrus fruit shell, cut in half crosswise. Carefully ream out the juice or cut out the flesh with a grapefruit knife. The edges of the shell can be notched with kitchen shears or a paring knife; for scallops, use a coin to outline the pattern; then cut around the pattern.