1. In a large, heavy pot, heat the oil over moderately high heat. Season the chicken with 1/4 teaspoon of the salt and add it to the pan. Cook the chicken until browned, turning, about 8 minutes in all. Remove. Pour off all but 1 tablespoon fat from the pan.
2. Add the onion, carrots, celery, and garlic to the pan. Reduce the heat to moderate and cook, stirring occasionally, until the onion is translucent, about 5 minutes.
3. Reduce the heat to moderately low and add the paprika, flour, and cayenne to the pan. Cook, stirring, for 30 seconds. Stir in the broth, tomatoes, the remaining 1 1/4 teaspoons salt, the thyme, and the bay leaf. Add the chicken and bring to a simmer. Reduce the heat and simmer, partially covered, until the chicken is done, about 20 minutes. Remove the bay leaf and add the parsley and black pepper.
Menu Suggestions: Serve the goulash with spaetzle, buttered noodles, or boiled or mashed potatoes.
Wine Recommendation: With this dish, it's natural to experiment with one of the increasing number of reds imported from Hungary. Try Egri Bikavér or a varietal such as a merlot or a cabernet sauvignon.