Dredge meat in flour until evenly coated, shaking off excess.

Melt shortening in a large, deep skillet over medium-high heat. Add meat and cook until thoroughly browned on all sides, 5 to 6 minutes. Add onion and garlic and cook until onion is soft, about 5 minutes. Add water, tomatoes, green chiles, salt, and oregano.

Cover, and simmer, stirring occasionally, until meat is tender, 1 to 2 hours. Remove cover and simmer until green chili sauce reaches desired consistency, 5 to 10 minutes more.