In a large straight-sided skillet or pot, cover chicken and onion with water by 1/2 inch; season generously with salt. Bring to a boil over high; cover, reduce heat to medium-low, and cook 5 minutes. Remove skillet from heat and let stand, covered, until chicken is cooked through (an instant-read thermometer should read 160 degrees), 12 to 14 minutes. Remove chicken from water and let cool completely. (To store, refrigerate in an airtight container, up to 3 days.)