All right, let's fix it!
Step 1: Clean the wound
Step 2: Form a tape trough
Step 3: Epoxy time!
Feel free to tap the rung a bit to dislodge any air bubbles and make sure that the epoxy fills up the gap.
This is a 5-minute Epoxy, but that name refers to the time for the epoxy to set. It will take a full 24 hours for it to cure.
Step 4: Hello again, chair
And you're done! Next time go a little easier on the furniture, OK?