Stir together the marinade and pour over the chicken strips. Toss to coat, then set in the refrigerator to marinate while you prepare the salad greens.
Stir the salad dressing ingredients together in a cup. Taste-test the dressing, looking for a tangy taste that is a balance between sweet and sour, salty and spicy (it should have some kick to it from the cayenne/chili). Add a little more sugar if it's too sour. Set aside.
Heat up grill and lightly brush grill with a little vegetable oil. Grill your marinated chicken, basting it with the left-over marinate the first time you turn it. For oven-broiling, place chicken strips on a broiler pan (or on a foil-covered cookie sheet, turning up foil at the edges to prevent spilling). Set oven to broil setting and place chicken on one of the upper racks, turning it every 3-5 minutes, or until well done.
For the mint and basil, stack the leaves on top of each other, then thinly slice into slivers and toss in with the salad. Add most to the salad and toss with most of the dressing. Portion out onto plates and top with the hot chicken strips. Drizzle remaining dressing over the chicken and top with remaining basil and mint. For those who like it spicy, minced fresh chili can also be sprinkled over.