Hey there!
If you right-click on the spawner, you can see 2 buttons, one is to remove the spawner (on the right) and the other one is to upgrade the spawner.
Once you hover over the chicken egg, you should see this:
On the bottom, you can see how much it costs for you to upgrade a spawner. If you got all the resources, click on the chicken egg and you should be able to upgrade the chicken spawner.