Cook potatoes in boiling water to cover 25 minutes or until tender. Drain well, and cool slightly. Peel potatoes, and cut into 1-inch cubes. Set aside.
Combine potatoes, beets, and peas in a large mixing bowl; toss gently until well blended. Combine vinegar, olive oil, onion, tarragon, chervil, parsley, salt, and pepper in a jar; cover and shake vigorously until well blended. Pour over potato mixture, and toss gently until well blended. Chill until ready to serve.