Heat 3 tablespoons of the oil in a wok or large skillet over high heat. Add the chicken, sprinkle with salt and pepper and stir-fry until browned and cooked through, 4 to 5 minutes. Remove to a plate.
Add the remaining 2 tablespoons oil to the wok, add the mushrooms (in 2 or 3 batches if necessary) and stir-fry until browned around the edges, 3 to 4 minutes. Add the carrots and stir-fry for 2 minutes, then add the garlic and stir-fry for 1 minute. Add the pineapple and stir-fry for 1 more minute. Add the sweet chili sauce and continue to cook until the liquid comes to a simmer. Finish with the lime juice.
Transfer to a serving bowl and garnish with the sesame seeds. Serve with rice.