Trim excess fat from chicken. If using breasts, slice each in half widthwise to create thinner cutlets. Pound each piece with a meat mallet or heavy pan bottom until roughly even in thickness.
In a small bowl, whisk together olive oil, lime zest, lime juice, minced garlic, honey, ground cumin, ground coriander, salt and pepper. Reserve 3 tablespoons of marinade in a separate bowl for basting. Do not let it touch the raw chicken.
Add chicken and remaining marinade to a large resealable bag. Seal and knead to coat evenly. Refrigerate for at least 30 minutes and up to 2 hours. Do not exceed 4 hours.
While chicken marinates, combine diced pineapple, cilantro, jalapeño, and red onion in a large bowl. Add lime juice and ground cumin. Season with salt and pepper and toss gently. Taste and adjust. Cover and refrigerate until ready to serve.
Heat grill or grill pan to medium-high (about 400°F). Oil the grates thoroughly using a paper towel soaked in vegetable oil held with tongs.
Remove chicken from bag and discard used marinade. Place chicken on grill. Cook 4 to 6 minutes per side, brushing the top with reserved marinade before flipping, and again after. Chicken is done at an internal temperature of 160°F.
Transfer chicken to a plate, cover loosely with foil, and rest for 5 minutes. Then slice or chop.
Serve chicken over coconut rice. Top with a generous spoonful of pineapple salsa and fan sliced avocado alongside. Serve immediately.