1. In a small bowl, stir together soy sauce, cornstarch, and lime juice until cornstarch dissolves. Set aside.
2. Rinse chicken; pat dry. Cut chicken into 1/2-inch strips; season with salt and pepper. Trim beans on both ends and chop scallions. Heat vegetable oil in warm wok or very large skillet. Add chicken, beans, and scallions, and stir-fry on high heat until chicken is white throughout, about 5 to 6 minutes. Use a garlic press to add garlic cloves to mixture, and stir-fry another minute. Reduce heat to medium.
3. Stir sauce mixture again to mix through and then pour into pan and cook, stirring, until sauce thickens, about 2 to 3 minutes. Serve immediately.
Variation: If you and your family prefer more sauce, add 1/2 cup of chicken broth to the sauce mixture.