In a large bowl or gallon-size Ziploc bag, combine all ingredients except for the chicken. Mix well.
Remove ½ cup of the sauce mixture and set aside for serving the chicken.
To the remaining sauce, add the chicken thighs, mixing well so that all of the chicken is submerged in the marinade.
Cover or seal and place in the refrigerator to marinate for at least 4 hours and up to overnight.
Heat grill to medium-high heat (400°F).
Lightly brush the grates with oil.
Place the chicken on the heated grill. Cook for about 10 minutes without turning or moving. Flip and continue cooking until the internal temperature of the chicken reaches 165°F (about 10 minutes more). Discard the marinade that the chicken was in.
When the chicken is about halfway done cooking, add the pineapple rings to the grill and cook until golden on each side.
Remove everything from the grill.
Brush the reserved marinade over the chicken. You can place the chicken under the broiler for just a few minutes to thicken the sauce, or heat the reserved sauce in a small saucepan on the stovetop to thicken it slightly and then brush it over the chicken.
Be sure you have cleaned under the grill grates before cooking. Lift the chicken out of the marinade and allow the excess to drip off before adding it to the grill - lots of marinade draining into the grill can cause unwanted flames and burn the chicken.
Taste the reserved sauce before brushing it over the finished chicken. You can adjust the seasonings. I sometimes like to add another tablespoon of brown sugar for a sweeter barbecue flavor.