Combine chicken, oil and oregano in a large bowl and toss to coat. Preheat a chargrill pan over high heat. Cook chicken for about 4 minutes each side or until cooked through. Set aside on a plate. Once cool enough to handle, slice chicken pieces in half on diagonal.
To make the dressing, combine all ingredients in a jar and secure lid. Shake well until combined. Set aside.
Cut some of the cherry tomatoes into slices, some in half and leave some whole. Scatter rocket, tomatoes, avocado, onion, olives and chicken on a serving board or platter. Drizzle with a little of the dressing and serve remaining dressing on the side.