Place the chicken breasts in a large saucepan, cover with cold water, and bring to a boil. Lower the heat and simmer for 12 to 15 minutes, depending on the thickness of the breasts. Drain and cool.

Cut the chicken into bite-size pieces and place in a large bowl. Add the onion, celery, and grapes.

For the basil cream: combine the garlic, basil, and lemon juice in a food processor or blender, and process until smooth. Add the mayonnaise, salt, pepper, and sugar, and pulse a few times to blend. Pour over the chicken and mix well, to coat all.

Distribute the lettuce among four serving plates. Top each with a scoop of the chicken in basil cream and serve.