Place finely chopped chicken in a medium bowl. (If you prefer very fine chicken salad, put chicken in food processor and process a few seconds until very finely shredded, but not a paste).
Add to the chicken the green onion, 1/2 C mayonnaise , rosemary, 1 Tbsp lemon juice, dijon and salt and pepper. Stir to combine. Add up to an additional 1/4 C mayonnaise if you prefer your chicken salad moister. Taste, and add additional lemon juice if you prefer more lemony flavor. Stir to combine. Store refrigerated for up to 5 days.