Is it possible for the Dragonborn to use CHIM and ascend to god hood like Talos did?

Talos was mortal once and so was Vivec. Talos achieved CHIM before ascending to godhood, how he did so is not known. Lorkhan used CHIM to create Nirn, but he destroyed himself doing so. Its also said that Vivec attained his god hood by learning the ability of CHIM from Molag Bal. Molag Bal shows an obvious knowing of CHIM, as it was him who showed Vivec how to use it ; Xarxes being the writer of the Oghma Infinium, would also be likely to have some knowledge on the concept of CHIM and that would also mean Hermaous Mora knows of it as well the other Daedric Lords because they are immortal gods.

So my question being, if Talos and Vivic could attain CHIM, is it possible that the Last Dragonborn can as well?

Some might tell you that they actually do, given the Black Books we're required to read along the Dragonborn questline and all the subtext in the questline itself.

It's my personal headcanon that they do, at least. (You want the lore forums, though. You're most likely to find someone far more knowledgeable on the subject there.)

Sure he can. Anybody who has CHIM could.

It's certainly possible. As monkey said, there are certain CHIM-ish undertones in the Dragonborn add-on. It could be pretty interesting if the DB replaces Talos as the new mortal-made-god Lorkhanish champion.

Varieties of Faith in the Empire mentions how many Nords could not look at Tiber without seeing a dragon. There's also the myth of Tosh Raka, who apparently took on the form of a dragon. If something similar happened to DB, it would help alleviate concerns about contradicting Skyrim player choices. Bethesda would likely be able to more easily address the DB in new lore.

The DB wins Skyrim one way or the other, takes the fight to the Thalmor, reforges a new empire, and enters the pantheon as a divine. It's plausible, and certainly my favorite of the possible outcomes for DB, as there are an enormous amount of parallels between the DB and Tiber Septim, and this recursive process of history repeating itself is a strong theme in ES lore.

The dialogue of the Greybeards seems to imply that the Dovahkiin was an avatar of Talos to begin with (not to mention Old Hroldan), so I don't think the Dovahkiin really even needs to achieve CHIM.

Also Lorkhan never actually achieved CHIM, he just attempted it.

I still standby the opinion that the LDB is infact a Shezarrine.. although many argue against it..