Preheat the grill to medium. You can use a grill plate if you don't have a grill.
Drizzle chicken with olive oil and season with salt and freshly cracked black pepper.
Grill the chicken. Cook for 3 minutes and then flip and cook for 3-4 more minutes until just cooked through. Transfer to a plate and set aside.
In two medium bowls, add the arugula, tomatoes, bacon, and avocados. Top with the grilled chicken and serve with the basil vinaigrette drizzled on top and sprinkled with chives.