Put the parsley, cilantro, oregano, garlic, and about ¼ cup of the olive oil into the food processor and pulse until the leaves are coarsely ground.
Add the red wine vinegar, paprika, salt, and pepper and pulse. Continue to pulse while drizzling in more olive oil. The sauce should have a fair amount of liquid, though some people prefer it to be a little more dry, so check for consistency to meet your preference.
Serve immediately. Store in a lidded jar for up to one month in the refrigerator. If the olive oil thickens up, just allow the chimichurri to come to room temperature before using.