I'd like to see them replace him with Arex, the "E. T." looking character from the cartoons.

Well, there is certainly no shortage of untalented Russian jews in the world. Consider him replaced already.

They'll probably have to kill off the character from future installments in the franchise. They could do it off-screen like they did with Leonard Nimoy (older Spock, I guess, in this canon) in the new movie. Or they could take the lazy way out and just never talk about him again like what The Dark Knight Rises did with the Joker

I'm pleased to hear Abrams' thinking on this (not pleased by the circumstances though, obviously). I think there's no way he can be replaced.
Presumably they'll have to kill the character off, and presumably off-screen. How they'll handle it well111c, I'm sure they'll find a mature way to handle it. Bloody sad, though.
You might very well think that. I couldn't possibly comment.

That's like saying - make Paul Walker's character die in a car crash in the next Fast & Furious. No one is going to do that. They'd get a lot of hate from the fans.
FF7 is actually one of the best examples of how to retire a character whose actor dies. The next Star Trek should do something similar.

They should CGI his face on the enterprise but have him be killed when the enterprise is attacked it's truly sad he'll never be able to do anything again

The character of Chekhov is integral to the star trek story and needs to continue. An cater can be replaced sad as it is, but an important character such as Chekhov cannot. They should recast and dedicate the next movie to Anton.

JJ Abrams just said no
http://www.torontosun.com/2016/07/14/jj-abrams-star-trek-wont-replace-anton-yelchin

Chekov wasn't in Season One of the show. Which character had his job then? Maybe they'll find a way. Either way, so sad.

I think the best option may be to not us Chekov after STB. I understand the desire to want the character there, this isn't some character they made up for this film, it's one if the original series main characters. Everyone really wants to see all seven of the TOS characters there. But they have the difficult, and frankly awkward job of getting someone else to play him if they want him there.
The new timeline gives them the flexibility to remove one of the core characters if it needs to happen for some reason. That would probably be the best option.

I guess new timeline does give that leeway, now that I think about it. You're right. It would just feel so wrong to me because Chekov, the character, has always been my favorite along with McCoy.

They could replace Chekov with a new character. This is a new timeline after all. The characters' fate is already different from the original timeline. I think, this would be preferable to recasting Chekov. And I do want more Star Trek movies with the rest of this great cast.
"Everyone is entitled to his own opinion, but not his own facts."

The can't do that because Chekov is Chekov. He is a part of the original crew, which these movies are about. That's like saying replacing Uhura or Sulu with some new equivalent person.
So the choices are recast Chekov, recast everyone, or stop making Star Trek AOS movies. I don't know which option I want.

If they continue, might just make up a character the equivalent of his.

I don't think that's possible, and I hope they never try.
Anton was one of a kind.

I hope not and I hope this will be the last one
Look like Tarzan talk like Jane! HAHA