Prepare rice according to the package directions.
Meanwhile, whisk vinegar, soy sauce, cornstarch and apricot preserves in a small bowl. Set aside.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add chicken and cook, undisturbed, for 2 minutes. Continue cooking, stirring occasionally, until no longer pink on the outside and just starting to brown in spots, about 2 minutes more. Transfer to a plate. dd the remaining 1 tablespoon oil, garlic and ginger to the pan and cook, stirring, until fragrant, 20 to 30 seconds. Add broth and bring to a boil, stirring constantly. Add vegetables, reduce heat to a simmer, cover and cook until the vegetables are tender-crisp, 4 to 6 minutes. Stir in water chestnuts and the chicken. Whisk the reserved sauce and add to the pan. Simmer, stirring constantly, until the sauce is thickened and the chicken is heated through, about 1 minute. Serve with the rice.