Preheat the oven to 350°F (175°C).
In a large bowl, mix the peanut butter, granulated sugar, and brown sugar until creamy.
Beat in the eggs one at a time.
Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the peanut butter mixture, mixing well.
Roll the dough into 1-inch balls and place them on an ungreased baking sheet.
Bake for 10-12 minutes or until lightly golden.
Remove from oven and immediately press a chocolate kiss into the center of each cookie.
Allow to cool on the baking sheet for a few minutes before transferring to a wire rack.