Heat the oil in a medium skillet over medium heat. Season the chicken breast on both sides with salt and pepper and cook, until lightly browned and cooked through, about 5 minutes on each side; let cool.
Meanwhile, bring a small saucepan of salted water to a boil, add the broccoli and cook until crisp-tender, about 5 minutes. Drain, rinse under cold water and set aside.
Chop the chicken and broccoli into bite-size pieces. In a large bowl, whisk together the mayonnaise, vinegar and curry powder. Add the chicken, broccoli, apple, dates and celery, and toss. Season to taste with salt and pepper and serve with pita.