Hull and wash strawberries and slice in half. Place into a blender or food processor and blend until the fruit is pureed. Measure out the required amount of puree. Transfer to a freezer-proof container and place in the freezer for 30 minutes.
Remove fruit puree from the freezer and return to the blender or food processor. Add the heavy cream, the half and half and the sugar and blend until the ingredients are well mixed.
Add this mixture to your ice cream maker and process according to manufacturers instructions. While ice cream is processing, melt chocolate chips in the microwave (about 1 1/2 - 2 minutes at 50% power). Stir until smooth and set aside to cool down a bit, but not so much it re-hardens. When ice cream is pretty much done processing and with churn still running, add melted chocolate to the ice cream in a steady stream and mix until combined with the ice cream. Transfer to a freezer container and freeze to harden.