It is not safe to wash chicken breast.
Washing chicken breast or any other raw chicken is not safe and not recommended as washing chicken breasts or other raw chicken can spread bacteria all over the kitchen and increase your risk of getting sick from cross contamination.
Chicken can simply be cooked directly without washing it and cooking the raw chicken fully will kill off any potential bacteria that could make you sick.
Professional chefs also do not wash chicken before cooking.
As health and food safety organizations also advise against washing chicken before cooking as washing the chicken when raw can spread bacteria all over.
Washing raw chicken can splash harmful bacteria like salmonella onto surrounding surfaces like hands, countertops, sinks etc and can result in cross contamination.
Instead of washing the raw chicken, chefs pat the chicken dry with a paper towel if necessary and then the chef cooks the raw chicken to the correct internal temperature of 165 F which kills any bacteria.
Other raw meats should also not be washed as it too can spread bacteria that is harmful.
You should also always wash your hands with soap and water after handling raw chicken and other meats to prevent illness and bacterial spread.