I've never had to medicate a chicken directly, but I have had to medicate many other animals.
The easiest way I found, if you can, is to use a bit of bread or other tasty treat to get her to eat the medication. I had a horse who refused ALL oral meds. He was also well over 16h tall and could raise his head almost 8 feet in the air. In order to worm him or give any other medication, I made him a PBJ sandwich.
Obviously Peggy is MUCH smaller, so she might only need a bit of tuna or a cracker to take her medication. I know she has some restrictions now, but I still feel that is much safer then trying to get liquid down a twitchy bird throat.