In a large nonstick skillet, simmer the jam, honey and mustard, stirring, over medium-low heat. Season the chicken with salt and pepper and cook in the skillet, turning frequently with tongs, until cooked through, 15 to 20 minutes.
Using a vegetable peeler, shave the carrots into ribbons into a large bowl. Add the peaches, bell peppers and greens.
Transfer the chicken to a cutting board and slice into strips, then return to the skillet, stirring to coat. Add the chicken and glaze to the vegetables; season with salt and pepper and toss.
