Can my neighbor legally come into my yard (without permission) and remove an existing chain link fence?

My advice is you will make your life easier if you avoid having disputes with your neighbors and should be willing to have a neighbor briefly go on your property if it will not harm your proerpty. As to taking down the fence, he can do this if it was on his property. WHo put up the fence, you or your predecessor in title? or him or his predecessor in title? If your predecessor did, even if the fence was on his property, you may have acquired the land by adverse possession. IF you do not want him to go on your property again, send him a certified letter stating this.

Generally, yes. The law permits an owner of abutting property to entire without it being deemed a trespass, however certain prerequisites are required. Regardless, the neighbor would not be allowed to damage your property and will have to repair any damage caused. If your chain link fence was damaged, there may be a claim. You should try to address this with your neighbor, as litigation amongst neighbors has many downsides. If it cannot be resolved, consider speaking to an attorney for legal advice as how to proceed.

Feel free to contact my office if you desire.

DISCLAIMER: This answer is provided in response to a "hypothetical" question and provided for general, informational purposes and does not create an attorney/client relationship. The information presented is not legal advice and may change based additional information and research. It is recommended that you speak to an attorney to discuss your specific legal issues.