1. Cook pasta in a large pot of boiling salted water, according to package directions, until al dente. Reserve 1 cup cooking water and drain pasta in a colander.
2. Lightly oil a ridged grill pan; place over medium heat. Season chicken with salt and pepper. Grill chicken for 6 to 8 minutes per side, until just cooked through. Transfer to a cutting board to cool slightly. Chop chicken.
3. In a large bowl, whisk peanut butter, soy sauce, vinegar, oil, crushed red pepper and ginger until blended. Season with salt and pepper to taste.
4. Add pasta and reserved water to bowl and toss to coat. Add chicken, cucumber and tomato; toss. Arrange pasta on a serving platter and garnish with scallions.