In a large heavy saucepan combine half of the berries and the honey. Bring just to boiling, stirring frequently; reduce heat. Simmer, uncovered, 5 minutes. Remove from heat.
Lightly mash berry mixture with a potato masher or fork. Stir in remaining berries, the cinnamon, and chia seeds. Bring just to boiling; reduce heat. Simmer, uncovered, 10 minutes or until thickened. Remove from heat. Remove and discard cinnamon stick.
Ladle jam into half-pint freezer containers, leaving a 1/4-inch headspace. Seal and store in refrigerator up to 3 weeks or freeze up to 1 year.