Are these bone-in, skin-on breasts, or boneless, skinless? Do you mean deep-fry (at least an inch of oil) or pan-fry (a film of oil in the pan)?
If bone-in, skin-on, deep-fry: heat the oil over medium-high heat till a drop of water sizzles, then put the breasts in skin-side down for about 15 minutes. Turn and cook the other side for another 15 minutes. Keep the oil bubbling lightly, to keep it hot enough that it doesn't penetrate the chicken. Remove a piece and cut it to check for doneness. If not done, put back in the oil and cook another few minutes, depending on how much pink you saw when you cut it.
If boneless, skinless, pan-fry: heat the oil over medium-high heat and brown both sides, about 5 minutes each. Add about 1/4 cup liquid - wine, chicken broth, water - cover, and cook for about 10 minutes, turning after 5 minutes. Cut it to check doneness and if not done, continue cooking a few more minutes, as above.
This just occurred to me: This last time, did you use a different method than the first time?
The trouble with eating Italian food is that five or six days later you're hungry again. ~ George Miller