Prepare noodles according to package directions.
While noodles stand, peel cucumber, and quarter lengthwise; discard seeds. Thinly slice cucumber.
Drain noodles, and place in a large bowl. Add cucumber, chicken, lettuce, bell pepper, and green onions; toss gently.
Combine basil and next 4 ingredients in a small bowl; stir well. Pour dressing over salad; toss well. Sprinkle each serving with nuts. Serve immediately.