Add the olive oil to an electric pressure cooker. Turn to saute, add the onion and ¼ teaspoon salt and saute for 7 minutes, stirring occasionally.
Add 2 sliced peaches, ¼ cup balsamic vinegar, garlic, chicken stock, chicken, and remaining ¾ teaspoon salt to the pressure cooker.
Secure the lid, select the manual setting, and set it to high pressure for 15 minutes.
When the pressure cooker timer is done, quick release the pressure.
Remove the chicken, and shred or chop into bite sized pieces. Add back to the pressure cooker, along with the remaining 1 tablespoon balsamic, stirring to combine with the sauce. Taste and add additional salt if desired.
Serve the chicken and sauce topped with 2 sliced peaches, a sprinkling of basil, and hot sauce to taste.