1. In a small frying pan, toast the pine nuts over moderately low heat, stirring frequently, until they are golden brown, about 5 minutes. Or toast in a 350° oven for 5 to 10 minutes.
2. In a small glass or stainless-steel bowl, using a fork, stir together the vinegar, garlic, lemon juice, mustard, 1 1/4 teaspoons of the salt, and 1/2 teaspoon of the pepper. Stir in the oil.
3. In a large pot of boiling, salted water, cook the rice until almost tender, about 10 minutes. Add the asparagus and cook until it and the rice are both done, about 5 minutes longer. Drain, rinse with cold water, and drain again. Transfer to a large glass or stainless-steel bowl.
4. Meanwhile, in a large frying pan, bring 1/4 inch of water to a simmer over moderately high heat. Sprinkle the chicken with the remaining 3/4 teaspoon salt and 1/4 teaspoon pepper and add to the pan. Cover, reduce the heat, and simmer, turning once, until cooked through, about 8 minutes. Remove the chicken, let cool slightly, and then cut into 1/2-inch chunks. Add to the rice and asparagus.
5. Add the tomato and red onion to the rice and then toss the salad with the dressing. Stir in the pine nuts just before serving.
Wine Recommendation: Vinegar and asparagus are hard to match with wine, but sauvignon blanc can handle both. Look for one from Friuli, Alto Adige, or Collio.