1. Rinse the turkey and pat it dry with paper towels.
2. Rub the turkey all over with the oil.
3. Sprinkle the breast lightly with salt and pepper to personal preference.
4. Place the breast, meaty side up, into a 5-quart slow cooker.
5. Peel the onion, cut it into quarter, and place the pieces around the edges of the pot.
6. Peel the garlic cloves and place them around the sides of the cooker.
7. Cover the cooker and cook the breast on low for 9 hours, or until a meat thermometer registers 170 degrees.
8. Remove the breast from the cooker and let the bird stand at least 10 minutes before slicing. (The internal temperature will continue to rise while the bird is standing.)
9. Discard the vegetables in the cooker.
10. Serve half the breast sliced, preferably with out the skins.