In a small saucepan combine water, vinegar, honey and salt. Bring to boiling, stirring to dissolve honey; reduce heat to medium-low. Add jalapeño. Cover and cook 2 minutes. Remove from heat; let stand 20 minutes. Drain, discarding liquid.
In a large bowl toss together chicken, cucumber, onion, mint, jalapeño and basil. Add melon, mango and avocado. Stir gently to combine.
For the dressing, in a small bowl whisk together coconut milk, basil, ginger, lime peel, salt and pepper.
Drizzle dressing over chicken mixture; toss gently to coat. Serve chicken salad in lettuce cups with a squeeze of lime.