For more crunch, serve coleslaw immediately; otherwise, let stand in the refrigerator 2 to 3 hours or overnight for the vegetables to wilt.
Place mayonnaise, vinegar, water, sugar, cayenne pepper, and dill seed in a medium bowl, and whisk to combine. Season with salt and pepper; set aside.
Combine cabbage, peppers, and chives in a large bowl. Add the reserved dressing, and toss to combine. Refrigerate until ready to serve.