1Remove turkey neck and giblets; discard large lumps of fat. With poultry shears or a knife, split turkey lengthwise along one side of backbone.
2Pull turkey open; place, skin side up, on a flat surface and press firmly, cracking breastbone slightly, until bird lies reasonably flat. Rinse and pat dry. (At this point, you may cover and refrigerate until next day).
3Before cooking, squeeze 1 to 2 lime halves and rub over turkey; sprinkle with oregano, then lightly sprinkle with salt and pepper.
4Barbecue turkey by indirect heat placing turkey, skin side up, on a lightly greased grill directly above drip pan.
5Cover barbecue and adjust dampers as necessary to maintain an even heat.
6Cook turkey until a meat thermometer inserted in thickest part of thigh (not touching the bone), registers 185ºF or until meat near thighbone is no longer pink; cut to test (1 1/-2 hours).
7Every 30 minutes, squeeze 1 to 2 lime halves and rub over turkey.
8Transfer turkey to platter.
9To carve, cut off wings and slice breast. Cut off legs and slice meat from thighs.