In a large bowl, combine milk, heavy cream, and sugar. Mix well until sugar is completely dissolved.
Add vanilla extract and 1 tsp of peppermint extract. Taste test the mixture. If you would like a stronger mint flavor, add 0.5 tsp more, taste test again. You can go even further and add another 0.5 tsp of peppermint extract. Usually 1 tsp of peppermint extract is enough to give a hint of flavor, which is what I normally use.
Add a few drops of food coloring and mix well. Keep adding only a couple of drops of food coloring until you're happy with the green color of your ice cream.
Your ice cream maker bowl needs to be frozen for 24 hours before using it. Once your bowl is chilled, set up your ice cream maker. I use Cuisinart's Ice cream maker which only has 2 plastic parts, one sits in the bowl to mix, and 1 as a lid.
Turn your ice cream maker on. Pour your ice cream mixture into the frozen bowl. Let it churn for 10 minutes.
While your ice cream is churning, chop up your chocolate chips. Chocolate chips are a little big for ice cream, so you could use mini chocolate chips instead if you like.
After 10 minutes of churning, add in your chocolate chips.
Let your ice cream churn for another 10 minutes.
Turn off your ice cream maker. Remove the ice cream from the frozen bowl, into an air tight container. Place it in the freezer for 3 hours prior to serving.