Combine 1/2 cup dill, 1/2 cup olive oil, 3 tablespoons lemon juice, shallot, and 2 teaspoons lemon peel in large bowl; whisk to blend. Season with salt and pepper. Add chicken and stir to coat. Marinate at room temperature 1 hour or chill up to 8 hours, turning chicken occasionally.
Combine mayonnaise, sour cream, 1/4 cup dill, 1 tablespoon lemon juice, and 1 teaspoon peel in small bowl; whisk to blend. Season with salt and pepper. Cover and chill until ready to use.
Steam potatoes until just tender, about 12 minutes. Transfer to large bowl; sprinkle with salt and pepper.
Combine zucchini slices and 2 tablespoons olive oil in medium bowl. Sprinkle with salt; toss to coat. Heat grill pan or large ridged cast-iron skillet over high heat until very hot, about 4 minutes. Working in batches, grill zucchini slices until just crisp-tender, about 1 minute per side; transfer to plate. Grill chicken until brown and cooked through, about 6 minutes per side. Transfer to work surface; cool 15 minutes. Cut chicken into 1/2-inch cubes; add to potatoes in bowl. Mix in celery, olives, and dressing; season with salt and pepper.
Overlap zucchini slices around edge of platter. Mound chicken salad in center.