After you've peeled and pitted the lychees (here's how), purée them in a blender or a food processor fitted with the blade attachment. It will not be 100% smooth, but get it as smooth as you can. Set aside. Pour the milk and cream into a medium-sized sauce pot and over medium heat and scald it. Tiny bubbles will appear on the edges of the pot and it should be very hot, but not boiling. Remove from the heat to cool a bit.
In a medium-sized mixing bowl, use an electric mixer or a whisk to whip the egg yolks with the sugar. Mix until it's very thick and is pale yellow. When you drizzle it with a spoon, it should rest for a moment before sinking into the rest of the mixture -- this is called the "ribbon stage."
Add the salt and vanilla, and then on a low speed, very gradually pour in about half of the slightly cooled cream mixture and blend until it's evenly combined. Pour this back into the sauce pot with the remaining cream mixture, and over medium-low heat, stirring almost constantly with a wooden spoon, cook until it becomes a beautiful, thick custard, about 6 minutes.
Remove from the heat immediately, let it cool for 15 minutes or so, and then stir in the lychee purée. Let this cool, stirring from time to time, for about 2 hours.
Pour into an airtight container and place in the refrigerator for at least 4 hours and ideally overnight.
Freeze according to your ice cream machine's directions.
Stir in the chocolate chips and serve! (Or mix in the chips and freeze until you're ready.)