Place the cut-up chuck roast into a medium bowl and sprinkle it with 1/2 teaspoon of salt and 1/2 teaspoon of pepper. Add the flour and mix until the flour coats all the beef pieces.
Over medium-high heat, heat two tablespoons of olive oil into a large soup pot or dutch oven.
Add the beef to the pot in batches and brown the meat on both sides. Place the cooked beef on a plate and set it aside.
Heat another tablespoon of olive oil in the same pot and cook the onions until translucent, about 3-4 minutes.
Add in the garlic and thyme into the onions, and cook for another 2 minutes or until the garlic is fragrant.
Into the pot, with the garlic, onions, and spices, add the Guinness (pour in the entire can), bring to a boil, and then reduce to a simmer.
While the Guinness is simmering, scrape up the brown bits on the bottom of the pot.
Stir in the tomato paste and beef stock and then bring to a boil.
Reduce to a simmer and add the potatoes, carrots, beef, and bay leaf.
Cook uncovered for 2 hours, stirring every half hour or so.
Cover the stew and cook for another hour.
Stir in 1 teaspoon of salt and pepper.
Serve hot with crusty bread.