Have all ingredients chilled.
Section oranges, reserving 2 tablespoons juice for dressing.
Reserve 4 orange sections for garnish; dice remaining orange.
Cut each pineapple in half lengthwise, through leafy top and all.
Cut a 1 inch thick lengthwise slice off each half, to make 4 slices complete with leafy tops.
Cut off lower third of each slice.
Pare and core cut off pieces and remaining unsliced pineapple; cut into chunks.
For salad, mix diced orange sections, 1 cup pineapple chunks, chicken, celery, and almonds.
For dressing, blend mayonnaise, 2 tablespoons reserved orange juice, salt, and marjoram; toss with salad.
Place two pineapple slices end to end and pile high with half the salad mixture.
Garnish with orange sections.
If you wish, add fresh strawberries, pink grapefruit sections, and honeydew melon balls, as well.
Repeat with remaining salad and pineapple.