Combine strawberries and agave in a heavy saucepan over medium high heat and bring to a boil. Lower the heat so that the mixture continues to boil gently. Stir the mixture a few times while cooking to prevent sticking or scorching and mash the berries a few times, a potato masher works well for this or you can use the back of a spoon.
Continue cooking for 25 minutes or until the berries have broken down and the mixture is very thick. Cool to room temperature. Mixture will thicken and gel up as it cools.