Whisk the pineapple juice, lime juice, vegetable oil, vinegar, garlic, oregano, salt, black pepper and chili together in a bowl.
Set aside ¼ cup (60 ml) of the marinade for brushing over the chicken during cooking.
Put the chicken pieces in a large zip-top bag or covered container. Pour the remaining marinade over the chicken and coat each piece well. Refrigerate for 4 to 8 hours.
Prepare the grill for two-zone cooking, with one medium-high area and one cooler area.
Remove the chicken from the marinade and discard the marinade that touched the raw chicken.
Put the chicken skin-side down over the hotter part of the grill. Cook for 4 to 5 minutes, or until browned. Turn the chicken over, then move it to the cooler area of the grill.
Cover and cook for another 25 to 35 minutes, turning every 8 to 10 minutes. Brush it occasionally with the reserved clean marinade.
Chicken breasts are ready when the thickest part reaches 165°F (74°C). Thighs and drumsticks have a better texture at about 175°F (80°C).
Rest the chicken for 5 minutes before serving or chopping.