Combine first 6 ingredients in a bowl; stir with a whisk. Add chicken, cantaloupe, and celery; stir gently. Cover and chill 30 minutes.
Divide salad greens and cucumber slices evenly among pita halves. Spoon about 1/3 cup chicken salad into each pita half. Serve immediately.
Wine note: This fabulous sandwich goes well with a glass of chilled white wine. The cantaloupe's fresh fruitiness calls for a wine that's equally fresh and fruity, without any toasty oak flavors to get in the way. A dry riesling is ideal. I love the Trefethen Estate Dry Riesling 2005 from Napa Valley, California ($20). --Karen MacNeil