In small bowl, mix butter and herbs until blended; set aside.
Season chicken with salt and pepper. In 10-inch nonstick skillet, heat oil over medium-high heat until hot. Cook chicken in oil about 5 minutes, turning occasionally, until no longer pink in center. Remove chicken from skillet; set aside and keep warm. To same skillet, add onion; cook about 3 minutes, stirring occasionally, until tender. Remove onion from skillet, set aside. Reduce heat to medium.
Spread generous half teaspoon herbed butter on outside of all of 4 bread halves. Place 2 halves in heated skillet, buttered side down. Top each with 1 slice cheese, 1 chicken breast, half of the onion and sliced tomato, and another slice cheese. Top with remaining pita bread halves.
Cook about 2 minutes, pressing down with spatula, until bottom is golden brown. Turn; cook about 2 minutes longer, pressing again with spatula, until cheese is melted. To serve, cut each sandwich in half.