In the bowl of a food processor, combine oats, peanut butter, dates, and vanilla until crumbly. With the motor running, add water a little bit at a time until desired consistency is reached. The mixture should hold together when pinched between two fingers.
Sprinkle salt and chocolate chips over the top and pulse just a couple of times to incorporate. Transfer the mixture to a sheet of parchment paper or a large plastic storage bag. Press the mixture together, then break off about one tablespoon of dough at a time, pressing and rolling it between your palms to form a ball. Store balls in an airtight container in the refrigerator for up to three days.