Place the chicken in a large saucepan with water, bring to a boil and cook until cooked through. Remove from heat, drain and let cool. Prepare a tablespoon of oil in a skillet over medium heat. Sauté the jalapeños, onions, and tomatoes until softened.
Shred the chicken and meat and place in the pan along with the tomatoes and chiles. Fry for a few minutes so that the chicken gains flavor. Put on each Tostada Charras a base of beans and approximately ¼ cup of the chicken tinga, and accompanied with slices of radishes or jalapeños to taste.