Preheat the oven to 425°F (220°C) and move the rack to the top third of the oven.
Cut the bell peppers and onion into 1/4-inch (6mm) slices.
Cut the chicken into 1/2-inch (1 cm) thick strips.
In a medium bowl, combine 2 tablespoons of oil with Fajita seasoning. Add the chicken and toss until evenly combined. Season with salt and pepper.
Heat the remaining 1 tablespoon of oil in a large frying pan over high heat. Add the chicken in an even layer. Cook it until browned then flip over and cook very briefly - do not cook the chicken completely, it should be browned but not cooked through (it will finish cooking in the oven). Transfer the chicken to a bowl and toss with lime juice.
Add bell peppers and onion to the pan. Cook for a couple of minutes until soft but still crunchy. Add the vegetables to the chicken, stir together and season with salt and pepper.