Cut each zucchini lengthwise into thin planks (about 5-6 per zucchini). Then cut each plank in half crosswise, and slice into matchsticks. Alternatively, you can use a spiralizer to turn your zucchini into zoodles.
Chop the onion half into small ¼-inch pieces.
Halve the lime, and cut one of the halves into wedges.
Slice the chicken breasts thinly.
Heat 1 tablespoon of oil in a 12-inch nonstick pan or wok.
Sprinkle chicken pieces with salt and pepper and add to hot pan. Stir into a single layer, and cook over medium-high heat until chicken is lightly browned and cooked through, about 5-8 minutes, stirring occasionally. Remove from pan.
To cook zucchini, heat butter in same pan, then add zucchini. Cook, stirring frequently, for 5-7 minutes, until zucchini is tender. (Zoodles and very thin matchsticks may cook faster.) Remove from pan.
Heat 1 tablespoon of oil in pan, then add chopped onions.
Add curry powder and ½ teaspoon salt and stir for 1 minute, then add chicken broth and coconut milk.
Cook for 6 minutes, until reduced slightly.
Add chicken and zucchini back to cream sauce and simmer until heated through.
Add juice from the lime half and stir. Serve with lime wedges.