Wash and peel the oranges, removing as much white pith as possible.
Separate the segments and remove any seeds.
If using pectic enzyme, place the orange segments in a bowl and cover with a solution made from 1 tsp pectic enzyme and 1 gallon of water. Allow the segments to soak for 3 hours, or overnight, stirring gently every once in a while to check on the progress of the enzyme. When the pith wipes away easily, rinse the segments to remove the remaining pith.
Prepare a waterbath canner and jars.
If using syrup, combine water and sugar in a saucepan and heat until dissolved.
Pack sterilized jars with orange segments, leaving ½ inch of headspace.
Pour hot syrup, water, or juice over the fruit, maintaining headspace.
Remove air bubbles and wipe jar rims clean.
Secure lids and bands, then process in a boiling water canner for 10 minutes, adjusting for altitude (see notes)
Let jars cool for 12-24 hours and check seals before storing.