Preheat oven to 350°F / 180°C / Gas mark 4.
Grind oats, then measure out 2 1/2 cups. Set aside.
In a medium bowl, combine egg with melted and cooled coconut oil. Whisk to combine.
Add a 10 oz. can of chicken, with the liquid, to the bowl with the egg. Use a fork to break up the chunks of chicken (if necessary) until it looks shredded. Use the fork to combine the egg mixture and chicken until it looks fairly uniform.
Sprinkle the 2 1/2 cups of ground oats into the bowl. Using a sturdy rubber spatula, stir the mixture until it forms a soft dough.
Place the dough between 2 sheets of parchment paper (or on a lightly floured surface) and roll out until dough is roughly 1/8" thick.
Use a cookie cutter to cut out shapes, then place them on a parchment-lined baking sheet. (I used a medium-sized cookie cutter. Yield may vary depending on the size of your cookie cutter)
Bake for 25 minutes, or until golden brown and baked through. Remove from oven and let cool completely on baking sheet.
Once completely cooled, store in an airtight container in the refrigerator.