To make the chicken, in a plastic bag or bowl, mix together the honey, soy sauce, olive oil, lime zest and juice, garlic, salt, and pepper.
Add chicken and mix thoroughly. Marinate for at least 1 hour.
While the chicken marinates, make the slaw. In a large bowl or serving platter combine mango, cabbage, jicama, and cilantro.
In a small bowl, whisk together the lime juice, brown sugar, olive oil, garlic, lime zest, and salt.
Pour the dressing over the slaw and toss until well combined. Let sit for 20 minutes so that the flavors can meld.
Preheat indoor grill or nonstick griddle over medium-high heat. Remove chicken from marinade and grill for 6 to 8 minutes per side, until juices run clear.
Serve warm over mango slaw.