Pat the chicken fillet dry with paper towels and season both sides with salt and freshly ground black pepper. Rinse the mixed salad greens and dry thoroughly. Halve the cherry tomatoes. Remove the pit from the avocado half, scoop out the flesh and slice.
Heat a grill pan over medium-high heat. Use a small amount of extra virgin olive oil to lightly grease the pan. Grill the chicken fillet for six to eight minutes per side until the meat is cooked through. Remove the chicken from the pan and let rest for five minutes on a cutting board.
Slice the rested chicken fillet into even slices. Whisk the remaining extra virgin olive oil together with the fresh lemon juice until a smooth dressing forms. Season to taste with salt and pepper. Combine the mixed salad greens, halved cherry tomatoes and avocado slices in a large bowl.
Distribute the sliced grilled chicken over the vegetables. Drizzle the dressing evenly over everything and toss briefly. Serve the salad immediately.