Heat oven to 350. Heat the oil in a 5 to 6 quart Dutch oven over medium high heat. Season the meat with salt and pepper. Add the brisket to the Dutch oven and brown on all sides. Transfer to a plate.
Add carrots, potatoes, onions and salt and pepper to the Dutch oven and cook, stirring occasionally until the vegetables start to soften, 5 to 7 minutes. Mix tomato paste with chicken broth. Add the broth, vinegar and Worcestershire sauce to the pot and stir to combine.
Nestlé the brisket in the vegetables and bring to a boil. Cover and transfer to the oven. Cook until the brisket is tender 3 to 3 1/2 hours. Let rest for at least 10 minutes before eating.
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