Put the frozen rice in a medium glass mixing bowl, and break it up using a fork. Drape a damp paper towel directly over the rice, and microwave until the rice is warmed through and softened, 2 to 3 minutes.
Meanwhile, puree the yogurt, oil, lemon zest and juice, mayonnaise, shallots, garlic, 1 1/2 teaspoons salt and a few grinds of pepper in a small food processor or a blender until smooth. Toast the walnuts in a small skillet over medium heat until fragrant and just starting to brown, about 2 minutes.
Combine the chicken, grapes, parsley and spinach in a large bowl, and toss with half the dressing. Add the warmed rice and toasted walnuts, toss again and serve with the remaining dressing.