What is the easiest way to remove chicken leg/drumstick tendons? I would like to make chicken drumsticks / legs (with skin on) easier to eat by removing the tendons and the fibula bone. Cook's Illustrated mentions this technique:


  
  Holding a paring knife just above the ankle and perpendicular to the bone, slice around the circumference all the way to the bone. This will expose the ends of about six thin white tendons.
  Using a clean pair of pliers, grip the end of each tendon and pull firmly to remove it. Repeat until there are no more visible tendons.
  


However when I use pliers and try to grip the tendon, they just slip. Is there something I am doing wrong?

I tried cutting the bottom tendon attachment and pushing the meat up and down and it is still very difficult/messy.
Based on your comments, the likely issue is with the pliers you're using.  I doubt that the relatively small set included in a multi-function knife is going to have enough grip to hang on to a slippery tendon.

I'd try a pair of (very, very clean) needle-nose pliers, like so:



They're readily available and inexpensive, so it's probably worth getting a dedicated set for the kitchen; these are also good for other fine, messy tasks like removing fish bones.  You should be able to get a much more secure grip on the tendons this way.  If they still won't pull out easily, try wriggling them back and forth a little perpendicular to the long axis of the bone.