Toast dried chiles in a dry skillet over medium-high heat until fragrant and blistered, 2 to 3 minutes per side. Remove stem and seeds; discard. Transfer chiles to a large measuring cup or bowl, and cover with hot water. Keep chiles submerged with a small bowl, and let soak for 30 minutes. Remove from water, and puree in a blender with 1/2 cup soaking liquid.
Heat a large heavy pot over high heat. Add 2 tablespoons oil. Season beef with 2 1/2 teaspoons salt and 1/2 teaspoon pepper. Brown beef in batches, adding more oil as needed, about 10 minutes. Transfer to a plate.
Add remaining tablespoon oil, the onions, garlic, and minced chiles to pot, and cook over medium-high heat until onions are translucent, about 5 minutes. (If the pan gets too dark, add a little water, and scrape up browned bits with a wooden spoon to deglaze.) Add cumin and oregano, and cook, stirring constantly, until fragrant, 30 seconds to 1 minute.
Stir in browned beef and chile puree. Add tomato puree, water, and 1/2 teaspoon salt. Bring to a boil. Reduce heat, and simmer gently, partially covered, until meat is very tender and juices are thick, 2 1/2 to 3 hours. (Check pot once an hour for excessive evaporation; if chili seems dry, add a little water.) Season chili with salt, and stir in vinegar. Serve immediately (or refrigerate for up to 3 days, or freeze for up to 3 months; reheat in a pot over medium heat, stirring occasionally).