In a large saucepan of simmering salted water, poach the chicken breasts until white throughout but still juicy, about 15 minutes. Remove the chicken and let cool. (The chicken can be prepared a day ahead. Wrap tightly and refrigerate.) Put the potatoes in a large saucepan of cold salted water. Bring to a boil and cook until tender, 10 to 15 minutes. Drain and rinse under cold running water. Remove the skins. Cut the chicken and potatoes into 1-inch cubes. In a large bowl, combine the chicken, potatoes and red pepper. In a blender or food processor, combine the basil, garlic, oil, vinegar, cheese and oregano. Puree until smooth. Season with salt and black pepper to taste. Pour the basil dressing over the chicken salad and toss to coat. Serve slightly chilled or at room temperature. chick 37