Place strawberries, agave, 1/4 cup chia seeds, and lime juice in a large bowl. Blend with an immersion blender until strawberries are chunky. Add remaining 2 tablespoons chia seeds and mix well with a wooden spoon.
Pour the mixture into two 1/2-pint canning jars. Allow to set in the refrigerator or freezer for at least 8 hours before consuming.