Preheat oven to 425 degrees Fahrenheit. Place pie crust in pie plate on a rimmed cookie sheet and poke holes in the bottom to allow steam to escape. If you have pie weights, it's also a good idea to line the crust with parchment paper and place them in the crust to keep it from puffing up too much.
Bake the crust for 10 minutes, or until very lightly golden. Remove and let cool.
Dump the chocolate chips in a large microwavable bowl and heat in the microwave at 50% power, stirring every 30 seconds until smooth. Let cool for 3 minutes.
Add the sweetened condensed milk, Irish cream, and eggs, and beat with a hand mixer until smooth. Pour into the prepared pie crust and spread evenly.
Bake for 15 minutes, then turn the temperature down to 350 degrees and bake for another 20-30 minutes. Keep an eye on the crust: if it looks like it's browning too much, cover with a pie shield or strips of aluminum foil.
Remove from oven when no longer jiggly in the middle. Let cool completely, then put in the refrigerator for 2 hours to chill.