Place the goat cheese and Greek yogurt in a food processor and process until fully combined, stopping and scraping down the bowl with a spatula once.
Add the chopped chives, basil, garlic powder, dried dill, and kosher salt. Pulse a few times until combined. Serve with crackers, crostini, bread, or vegetable sticks. Refrigerate for up to 2 days (tastes best the day of making).