1. Light the grill or heat the broiler. Coat the chicken with 1 tablespoon of the oil and season with 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Grill or broil until just done, 4 to 5 minutes per side. Let the chicken rest for 5 minutes and then cut crosswise into 1/4-inch slices.
2. In a large pot of boiling, salted water, cook the fusilli until just done, about 13 minutes. Drain, rinse with cold water, and drain thoroughly. In a large bowl, toss the pasta with 1 tablespoon of the olive oil.
3. Add the chicken, artichoke hearts, scallions, parsley, the remaining 5 tablespoons oil, the vinegar, the remaining 1 teaspoon salt and 1/4 teaspoon pepper, and the Parmesan to the pasta and toss well.
Wine Recommendation: Artichokes can be tough on wine since they tend to make even the driest ones taste sweet. To counteract this tendency, try an acidic white wine such as a Sancerre from France (made from sauvignon blanc grapes) or a sauvignon blanc from northern Italy.