Submerge bamboo skewers in water for at least 20 minutes to prevent charring during the cooking process.
Place chicken cubes in a bowl and toss with 1/4 cup of the barbecue sauce until evenly coated.
Thread chicken pieces onto the soaked skewers, approximately 5-6 pieces per skewer.
Heat a grill or indoor grill pan to medium-high heat and lightly coat with oil.
Grill skewers for 12-15 minutes, turning occasionally and brushing with the remaining barbecue sauce, until internal temperature reaches 165°F (74°C).
Prepare the dressing by combining avocado, Greek yogurt, lime juice, garlic, cilantro, salt, and pepper in a food processor; pulse until smooth.
Assemble the salad by layering romaine lettuce, tomatoes, cucumber, and red onion in a large serving bowl or individual containers.
Remove chicken from skewers or place skewers directly on top of the prepared salad.
Drizzle with the creamy avocado dressing immediately before serving.