Cook the bacon with 2 Tbs. of the oil in a large Dutch oven over medium heat until it renders most of its fat and starts to brown, about 5 minutes. Season the sliced chuck steak with 3/4 tsp. salt, raise the heat to high, and sauté the beef until it loses its raw color and starts to brown in places. Add the ground beef and sauté, stirring, until it loses its raw color, about 3 minutes. Transfer to a large plate and lower the heat to medium-high.
Add the remaining 2 Tbs. olive oil and the onions to the pot, season with 3/4 tsp. salt, and cook, stirring often, until the onions soften and start to brown, about 6 minutes. Add the garlic, jalapeño, and chili powder and cook, stirring for 20 seconds. Add the beer and cook, stirring, until the beer reduces by about half, about 3 minutes.
Put the beef back into the pot and add the tomato purée and chicken broth. Bring to a boil, then reduce the heat to a gentle simmer (between low and medium-low heat) and cook, stirring occasionally, for 1 hour. Stir in the beans, 1/4 cup of the chopped cilantro, and the oregano, and cook for 20 minutes more. Taste for chili powder, salt, and pepper. Keep warm until serving.
Just before serving, zest and juice the lime. Mix the remaining 1/4 cup cilantro, the lime zest, and 2 tsp. of the lime juice with the sour cream. Season with salt and pepper and more lime juice to taste. To serve, ladle the chili into large bowls and top each with a dollop of sour cream and a little more cilantro and lime.
If you want to make the dish ahead, let it cool down at room temperature and then refrigerate for up to 3 days. Reheat over low heat until it’s hot throughout.