Recently a slew of new complaints regarding Pokemon Go have been showing up all over the internet over people somehow being able to place a Pokemon egg in gyms. Now since eggs have no CP or HP there is no way to defeat them and therefore no matter how hard you try you won't be able to claim the gym as your own.
Clearly there will be a future update which will prevent this from happening and when it does a lot of gyms will be up for grabs, but until then you can't do a thing about the gyms. You can however send a report to Niantic, but by now they should be fully aware of this issue plaguing Pokemon Go players.
Now there is no word on what will happen to the players exploiting this glitch once the new update comes out but with Niantic's recent methods of handling third party apps and the accidental distribution of legendaries I'm sure that the cheating players will experience some sort of penalty, especially as while this issue is being fixed those players are racking up rewards for nothing.