Rinse the hominy thoroughly with plenty of water.

In a large pot, cook the chicken breast and hominy with the onion and garlic in 10 1/2 cups water (2 1/2 liters). Cover and simmer over medium heat until the hominy is tender and has 'bloomed.'

Remove the cooked chicken breast and shred it.

Serve the broth and hominy in a pozole bowl, then top with the shredded chicken.

Add lettuce, radishes, oregano, and a squeeze of lime to taste.