Heat a grill over high heat. Season the chicken with the vegetable oil, salt and pepper. Grill until nicely charred on one side, about 3 minutes, then turn and repeat on the second side. Lower heat to medium and continue to cook, turning from time to time until the chicken is cooked through, about 15 minutes all together. When cool enough to handle, chop or shred the chicken and place in a large bowl.
While the chicken is cooking, bring a large pot of salted water to the boil. Add the collard greens and cook until softened, about 8 minutes. Remove greens (save water for the pasta) and add to bowl with chicken. Cook the pasta according to package directions to al dente. Drain, rinse under cold water to stop the cooking and add to the bowl. Add the black-eyed peas and onion.
In a small bowl, whisk together the BBQ sauce and yogurt. Stir into other ingredients. Season to taste with salt and pepper.