Here is my meal under $3: The Fast. Cost: $0.
I know this is cheating, but I usually only eat once per day at dinner (a la the WarriorDiet), so most of my meals exceed $3. But if you allocate the cost among the standard 3 meals, many would fall under the $3 threshold.
Or, how about this meal?
Cup of coffee with 1-2 Tbsp of unsalted butter or coconut oil. When I have a slight hunger pang in the morning, this is my go-to meal. It lasts me until dinner. Cost: ~$1.
The beauty of primal is that while individual meals may cost above average, the overall cost remains low due to frequent home cooking and infrequent snacking. Not to mention the long-term savings from avoiding the diseases of civilization.