Before you get a new one, I would want to know why the other one died. If she died of something contagious (like Giardia), you could be condemning the new chin to a certain death.
Since the cause of her death is in question, I would (1) watch the male carefully, especially water intake, amount of food eaten and what the poop looks like (2) clean the cage and sterilize everything in it (3) dispose of any food or hay on hand and replace it with new.
Usually, when one dies, I strongly suggest that everything in the cage, as well as the cage, be sterilized and anything that is porous (like wood) be replaced as a precaution only.
How will your chin that has just lost it's mate react to a new chin?
This is one area many answers are true.
Each chinchilla has it's own personality. Each one may react differently to the same situation and to the new chin you introduce to them.
Some prefer to stay alone, others prefer company.
Some will accept another mate while others will kill a new one when introduced (to soon or to late may not make the difference).
Some will accept a kit or a young chin, while others may even kill it.
A slow introduction is in order, regardless. Play times together, but separate cages until you are sure they will accept each other.
If it were your female that is still living, I would suggest a kit or very young chin.
It being your male that is still living, maybe a young male.
If you want him to have a female mate ... I would NOT put a female in with him that is
under a year old. You do not want to get a female pregnant that is under a year old.
Is it ever to soon or to late? Yes, that can be a factor ... one that can not be answered until you try.
I have had many that can't stand to be alone and will readily accept a new cagemate.
While other times, I have had chins that take a month to several years before they will accept a new cagemate.
And some that will not accept a new cage mate - ever. This one is the one to be cautious of ... the 'nonacceptance' can be anything from ignoring the new cagemate to killing the new cage mate.
Lots of things to consider ... most of which are strictly trial and error with allot of supervision and patients.
Sorry I could not give you a more exact answer ... but I don't think anyone can, without being right there to see the reactions.
We can share our own experiences, but, to know for sure what your one male chin will do is unknown.
Jo Ann