Drill two 1/4-inch holes through one side of the planter, 1 inch below the rim. Space the holes to coordinate with the width of the facing side of the planter, less 1/2 inch on each side. For example, if you are attaching a 10-inch long rectangular planter to the fence, drill a 1/4-inch hole through the 10-inch long side, 1/2 inch from each outside edge and 1 inch below the top rim. To attach a round planter to the fence, space the holes as far apart as possible along the front of the planter. Make sure that you use the correct drill bit for the planter material; a ceramic bit for ceramic planters and a wood bit for wood planters.
Drill two 1/4-inch holes on the opposing side of the planter so that they line up with the first two holes. For round planters, place the holes directly across the planter from the first two.
Measure a length of 22-gauge craft wire to fit through the two opposing holes on one side of the planter, across the facing side of the planter and then straight through the second set of holes. Add 12 inches to the measurement. Cut the wire to the measurement.
Insert one end of the wire through the opposing holes on one side of the planter. Leave 6 inches of wire extending from the hole on the back of the planter. Bend the wire to fit the shape of the front of the planter. Insert the wire through the second set of opposing holes. The wire should be running through the top of the planter on both sides; each side should have 6 inches of wire extending through the holes on the back.
Insert the wires through the holes in the chain link fence. Adjust the wires so that they fit in the V of the links on the fence. Wrap each 6-inch section of wire around the wire on the chain link fence securely to attach the planter to the fence.