In the bowl of a 6-quart slow cooker, stir together crushed tomatoes, tomato paste, olives, capers, chopped anchovies, red wine vinegar, oregano, garlic, red pepper flakes, and water.
Heat a Dutch oven or skillet with oil over medium-high heat.
While skillet is heating, season chuck roast on both sides with some salt and black pepper.
Add roast to heated skillet and sear on both sides until deep golden brown and lightly crusted, about 5 minutes per side.
Nestle beef into sauce in the slow cooker.
Cover and cook on low for 10 to 12 hours, until beef can be easily shredded with a fork. (Note: I do not recommend cooking the sauce on high. Tomato sauce has a tendency to burn if cooked on the slow cooker’s high setting. Even on low, you may still get some browning around the edges of the sauce.)
Use two forks to shred meat right in the slow cooker. Stir everything together to combine. Taste sauce and season with some salt and pepper, if needed.
Serve sauce over pasta, rice, or polenta. (Note: For an easy serving option for a crowd, cook 1lb of spaghetti and stir it directly into the sauce in the bowl of the slow cooker. You can leave the slow cooker on the warm function and serve the sauce and pasta whenever you’re ready.)