Hello,
You have plethora of options after doing B.Sc in Chemistry hons. You can go for a B.ed if you want to become a teacher. Or choose M.Sc in chemistry and do research work later on. For that you need to appear for JRF exams.
You can go for a job in private or government sector too, as per your wish. 
For private jobs, you can join pharmaceutical companies, or any other healthcare related companies. There are food corporations which you can join, or you can go for the oil and gas industry. There are so many options in private sector.
If you wish to go for government sector, then you can appear for various exams. But you need to prepare well for that.
Also, you can apply for upsc exam if you wish to go for civil services.
You can do an MBA after completing your B.Sc, that is also very beneficial to get you good packages in the private sector.
So, there are so many options you have. You can choose whichever you find the most suitable for yourself.
Hope this helps, good luck!

hey rishu 

first off all i can tell you bsc chemistry has more job opportunities than bsc physics,biology ,zoology,and i think even than maths depend upon the college. after bsc you will be able to give many staff selection exams  but i will prepfer to go for msc from some iitS .also here are other answers 

https://www.careers360.com/question-what-can-i-do-after-bsc-chemistry

best wishes