I'd say it has more in common with medicine and vivomancy (historically part of alchemy, specifically as relating to the homunulus; essentially the magic of creating life from inanimate matter) than it does with chronomancy.
Chronomancy would have more in common with illusion magic, and space-distortion magic.
Regardless, without also trancending several physical design issues with existing neural hardware, immortality would become unbearable over sufficient periods of time. Specifically, after you are about 25, the vast majority of your primary axons are formed, making the learning of new skills substantially more difficult. The brain's design is not meant to endure eternally. Eventually the immortal person would suffer such extreme culture shock, and have such dated skills, that they would be unable to engage in a society that they no longer recognize.
Take for instance, if you plucked an illiterate dark-age peasant from backwater romania, and dropped them in modern-day new york. That's just 500 or so years of time passing, invoking a tremendous change in the ways people live, work, and play, and a huge shift from agrarian skills based living to information skills based living.
Said theoretical immortal would struggle terribly trying to keep his/her skills up, as the hardwired connections in his/her brain become less and less relevant over time. Truly, a relic of ages past, living in the past, and unable to let go.
This means that said immortal needs to have radical neural pruning and radical neurogenesis going on to keep up over the passing ages, which means he/she will be forgetful, and literally lose skills and knowledge they used to be proficient with as time passes, in order to stay plastic enough to keep gaining new ones and adapting to the changing world.
Such radical plasticity would make it likely that the person would have a highly mutable personality as well, as the memories that form the basis of behavior and decisions would literally be lost and replaced over time.
The person from 1412 would be radically different than the person from 2012. They probably won't even remember what it was like in 1412 by that time. Diaries would be essential.