Heat gas or charcoal grill. In gallon-size resealable food-storage plastic bag, mix oil, lime juice and 1 tablespoon taco seasoning mix until smooth. Add chicken; seal bag. Shake until chicken is evenly coated.
Place chicken on grill over medium heat. Cover grill; cook 12 to 15 minutes, turning once, until juice of chicken is clear when center of thickest part is cut (at least 165°F). Let stand 5 minutes.
Meanwhile, in 2-quart saucepan, heat beans, salsa and cilantro over medium heat, stirring occasionally, until hot. Remove from heat; cover and keep warm.
Cut chicken crosswise into strips. Divide chicken on half of each tortilla; top with bean mixture. Fold other half of tortilla over filling.