Remove the chicken fillet from the refrigerator and let the meat come to room temperature. Preheat a dry grill pan on the stove until it is very hot. Break or chop the pecans into slightly smaller pieces. Make sure the mixed greens are dry and ready in a large bowl.
Place the chicken fillet in the hot grill pan and grill the meat for about ten to twelve minutes until completely cooked through. Turn the fillet halfway through cooking so both sides get dark grill marks and the inside is cooked through. Remove the chicken from the pan and let it rest for a few minutes on a cutting board.
Slice the grilled chicken fillet with a sharp knife into equal cubes. Add the chicken cubes together with the pecan pieces to the bowl with mixed greens. Mix the tablespoon of olive oil and a dash of lemon juice in a small bowl. Pour this dressing over the ingredients in the bowl and toss everything together thoroughly.
Divide the prepared salad among the plates. Make sure the chicken cubes and pecans are distributed evenly over the portions. Serve the dish immediately so the chicken pieces are still lukewarm.