In a saucepan, combine the chopped fresh pineapple, water, and granulated sugar.
Place the saucepan over medium heat and stir the mixture until the sugar dissolves completely.
Bring the mixture to a gentle boil, then reduce the heat to low and let it simmer for about 10-15 minutes, or until the pineapple pieces have softened and released their juices.
Use a potato masher or the back of a spoon to mash the pineapple pieces further and extract more flavor.
Remove the saucepan from the heat and let the pineapple syrup cool to room temperature.
Once cooled, strain the syrup through a fine-mesh sieve or cheesecloth to remove any solids and obtain a smooth syrup.
Transfer the pineapple syrup to a clean glass jar or bottle for storage.