Soak beans in cold water in a large pot for at least 8 hours or overnight. (Alternatively, cook beans in boiling water for 2 minutes. Cover and set aside for 1 hour.) Drain and rinse beans.
Heat oil in a Dutch oven over medium heat. Add onions, carrots and celery; cook, stirring occasionally, until softened, 5 to 10 minutes. Add garlic, cumin and oregano; cook, stirring, until fragrant, about 1 minute.
Add water, bay leaf and beans; bring to a simmer. Skim foam from surface. Cover and simmer over low heat, stirring occasionally, for 1 1/4 hours.
Meanwhile, lightly toast chiles in a heavy dry skillet over medium-low heat. Transfer to a plate and let cool; tear into several pieces.
Bring broth to a simmer in a small saucepan. Remove from heat and add chiles; cover and let soften, turning several times, for 30 minutes. Transfer chiles and broth to a blender or food processor and puree until smooth.
When the beans have simmered for 1 1/4 hours, add chile puree, tomatoes, barley and salt. Simmer, partially covered, stirring occasionally, until beans and barley are tender and chili has thickened, about 45 minutes more.
Remove bay leaf. Season chili with vinegar, sugar, pepper and salt. Serve with Avocado Salsa, if desired.
2 1/2 starch, 2 vegetable, 1 lean meat