In a small saucepan, heat ½ cup chicken broth until it starts simmering (but not boiling).
While chicken broth is heating, in a medium bowl, sprinkle gelatin over remaining ¼ cup of chicken broth. Let sit for about 2 minutes.
Pour hot chicken broth into bowl, stirring or whisking constantly, until granules are all dissolved and no clumps remain. Stir in finely diced chicken.
Place molds on a cookie sheet or other solid surface that will fit in fridge (this will make it easy to transport filled molds to fridge). Pour or spoon mixture into prepared molds, filling each to the top edge.
Place molds in the fridge for about 1 ½-3 hours, depending on how big your molds are, until set. Test by touching jello with your finger. If your finger sticks, jello needs more time in the fridge.
Carefully pop jello out of molds by pressing on backs of molds to release.
Store chicken jello treats in an airtight container in the fridge for 3-4 days.