In a mixing bowl, combine the peanut butter, powdered sugar, vanilla extract, and salt. Mix until smooth and well combined.
Using your hands, shape the mixture into egg shapes, about 1 inch long. Place the shaped eggs on a parchment-lined baking sheet and refrigerate for at least 30 minutes to firm up.
While the eggs are chilling, melt the chocolate chips and vegetable oil together in a microwave-safe bowl. Heat in 30-second intervals, stirring in between, until completely melted and smooth.
Remove the peanut butter eggs from the refrigerator. Dip each egg into the melted chocolate, ensuring it is fully coated. Return the coated eggs to the parchment-lined baking sheet.
Once all the eggs are coated, refrigerate again for about 15 minutes to set the chocolate.
Serve immediately or store in an airtight container in the refrigerator for up to one week.