The cooking time for poached chicken varies depending on its size and the fat content. It would take about 10-15 minutes to fully cook medium sized cuts poultry. Some of the fats in the meat will start to melt that’s why you’ll see some oil in the water. But just to be sure, you can check on the doneness of the chicken by inserting an instant-read thermometer into the thickest part of the meat. It should read at 165 degrees F.