Combine chicken breasts with onion, salt, pepper, bay leaf, and water in a large saucepan; cover.
Simmer 30 minutes, or just until tender.
Remove from broth, cool until easy to handle, then pull off skin.
Remove meat from each half of breast in one piece; place in one layer in a shallow dish.
Chill.
Strain broth into a 2-cup measure chill just until fat rises to top, then skim
Soften gelatin in 1 cup of the broth in a small saucepan.
(Save any remaining to add to soup.) Heat gelatin mixture, stirring constantly, just until gelatin dissolves; pour into a small bowl.
Blend in mayonnaise or salad dressing; chill, stirring several times, 20 minutes, or until as thick as unbeaten egg white.
Spoon part over chilled chicken breasts to make a thick layer, then repeat with remaining until chicken is evenly glazed.Cut each olive into 6 slivers, arrange petal fashion, on top of each glazed chicken breast; chill until gelatin is firm.
Cook lima beans, following label directions; drain.
Toss with 1/4 cup of the Italian dressing in a small bowl; cover.
(This much can be done early in the day, or even a day ahead.)
When ready to serve, place salad greens in a large shallow bowl; drizzle remaining 1/4 cup Italian dressing over; toss lightly to mix.
Top with tomato slices; mound lima beans in center, then arrange chicken breasts, spoke fashion, around beans; place quartered eggs around edge of bowl.
Garnish with a cherry-tomato flower, if you wish.
To make, cut a cherry tomato into eights from tip almost to stem end; separate "petals" slightly; stuff with a ripe olive and top with a sprig of parsley.