In a saucepan over medium heat, add berries, zest, juice, and syrup. Cook, stirring occasionally, for 5 minutes. Lightly mash berries with a spoon.
Increase heat to medium-high and bring to a boil. Cook, stirring occasionally, until reduced by half, approximately 5 to 10 minutes.
Add chia seeds, continue to boil for 1 minute.
Transfer jam to heatproof jars or containers and allow to cool.
Cover and keep in refrigerator up to 2 weeks or in freezer up to 3 months.