Prepare your grill (either charcoal or gas) for direct high heat. Or right before cooking, heat a griddle or large cast iron frying pan on the stovetop.
Combine the turkey, bread crumbs, mayonnaise, chives, green onions, Worcestershire sauce, chili sauce, basil, salt and pepper in a large bowl and work the mixture with your hands to just mix. Do not over mix or the burgers will be tough. Form the mixture into 4 1-inch thick patties.
Season both sides of the patties with salt and pepper. Grill them for 5-7 minutes on each side, until the internal temperature of the patties reach 170°F on a meat thermometer.
Turkey burgers should be cooked through, not rare. Toward the end of the cooking, put the buns on the grill to toast for about a minute. Remove the burgers from the grill to a platter, cover and let rest for 5 minutes.