Slice 1 chipotle pepper open and remove the seeds. Add pepper and all of the adobo sauce from the can to an electric blender along with onion, cilantro, and garlic; reserve remaining peppers for another use. Blend until smooth.

Heat oil in a Dutch oven over medium-high heat. Add chicken and cook until golden brown, turning as needed, about 5 minutes. Mix in the blended chipotle sauce. Season with cumin, cayenne, salt, and black pepper. Pour in water to cover chicken. Reduce heat to low and simmer until chicken is easy to shred, about 2 hours.