Using a sharp knife, cut the breast halves in half crosswise, then lengthwise into strips 1/2 inch wide.
Blend salt, pepper, oregano and the flour well in a flat dish. Add chicken pieces in one layer. Stir to season, keeping each strip separate.
Heat butter and oil over high heat in a skillet large enough to hold the chicken pieces in one layer. Add chicken, cook and stir until lightly browned, about 3 minutes. Add the tomatoes and garlic and cook, stirring, for 3 minutes. Add the coriander and lime juice and continue cooking. Blend well and serve immediately. Serves 4.