Thread chicken and green onions onto 8 (10-inch) skewers (see Note), evenly dividing pieces.
In a wide, shallow container, such as a 9- by 13-inch baking dish, combine oil, cumin, oregano, garlic, and 1/2 teaspoon salt. Add skewers and turn to coat all sides with oil mixture. Cover and chill at least 30 minutes or up to 4 hours; turn skewers occasionally.
Meanwhile, grate 1 teaspoon of peel from orange into a bowl. Cut away and discard remaining peel and white membrane from orange. Cut between segments to release fruit. Cut fruit into 1/2-inch chunks and put in bowl with peel.
Chop dark green onion tops and add 1/2 cup to bowl with orange; reserve remaining tops for other recipes. Peel and pit avocadoes; cut into 1/2-inch chunks and add to bowl. Stir in lime juice, cilantro, remaining 1/4 teaspoon salt, and jalapeño to taste. With a fork, mash mixture to desired texture -- less for a chunky guacamole, more for a smooth one.
Place a nonstick grill pan over high heat. When pan is hot, in 2 to 3 minutes, lay skewers in pan without crowding. Cook, turning to brown evenly, until chicken is no longer pink in thickest part when cut to test, about 8 minutes total. Serve hot with citrus guacamole to spoon onto portions.
Nutrition information per serving: