Inspect 2 jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until fennel is ready. Wash new, unused lids and rings in warm, soapy water.
Place sliced fennel in a colander and rinse well.
Combine water, vinegar, and salt in a large saucepan and bring to a boil. Add the fennel, sugar, olive oil, and chives; stir to combine. Bring back to a boil and cook for 3 minutes.
Remove fennel from the cooking liquid with a slotted spoon and pack into sterilized jars. Fill the jars with the hot cooking liquid, leaving 1/2-inch head space. Wipe the tops of the jars with a clean cloth. Place lids on the jars and tighten.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 15 minutes.
Remove the jars from the stockpot with a jar lifter and let rest on a kitchen towel, several inches apart, for 12 to 24 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area for 1 week before consuming.