Are there immortal people living on Earth?

Well, they wouldn't be dying on Earth.

If you are immortal they aren't people, but I can't tell you if their are beings that live longer than other beings. Sometimes I wonder if our consciousness is kinda like a TV show. We think we are alone in all of our thoughts and observations but "unseen" forces like individual light particles, radio signals and other remote places unprovable, and currently undetectable by human beings could be keeping and learning from all of our experiences vicariously. If this dimension or what ever it may be does work this way it could help us fill in a better understanding of the world as a whole, and why it is whole. If no one ever made note of the water cycle, how would we be able, without first experiencing it be able to tell that a cloud, a snowball, dew on plants in the morning, underground water, the ocean, mist, rivers, the stuff atop mountains ETC. was all just water. The human soul could work in a similar fashion, or not. IDK, but when good things happen and happiness is felt, a journey to keep that may inspire a desire to exist, and who knows how may ways in which humans do this. A piece called Barber's Adagio for strings is about the water cycle where rivers make their way to the ocean. People report that this music causes emotional dissonance and catharsis. Why that is, and that it isn't the point that the composer was aiming to portray tells us something about ourselves. Their may be more to us than we realize. 

Immortal people>IDK, but it would be kind of cruel of them to understand who they had achieved enough flawless or possibly just slowed regeneration of cells, and tell no one else. If they did I could see their fears though. I mean their is no new innovation that humans weaponize and threaten others with. Humans don't see the value in each other, beyond what that person can offer them, and even then we rob others of anything good that we envy. Envy is a huge issue, so an immortal person may remain silent about it jest so that the hate and envy people use to better their situation at others expense, could be a reason they withdrawal from the public. Heck we don't even have enough good will to assure that people don't die alone and unabused by the medical "professionals" who have the word CARE in their professions title. Yup people a scum sometimes, and other times the are heart warmingly kind. Immortal, nope. Not as far as I'm privy to. 

Maybe their are, God does amazing things! Jesus said to a disciple what is it of you if I let that person live forever of the world

People, by their very nature are not immortal.

No, they are all buried underground.

Most likely.  They'd live forever if they managed to avoid certain fast-acting diseases,  and other misadventures like accidents, wars, and murder.  Sadly, most of them do not.

(Well...sadly for THEM)

Not since the 80s

queen elizabeth ii