To prepare vinaigrette, combine first 8 ingredients in a jar. Cover jar tightly, and shake vigorously; set aside.
To prepare salad, bring water to a boil in a medium saucepan. Add the wild rice; cover, reduce heat, and simmer 1 hour or until tender.
Combine apple wedges and 1 1/2 tablespoons lemon juice in a small bowl, and toss well. Heat a nonstick skillet over medium-high heat; add apple mixture. Cook for 6 minutes or until tender, stirring frequently.
Combine cooked wild rice, arugula, chicken, grapes, and cheese in a large bowl. Add the vinaigrette, and toss well. Place 1 1/2 cups salad on each of 4 serving plates, and top each serving with 4 apple wedges.