Yes it's possible to live a normal happy and healthy life with only one Kidney.
Some people are born with only one Kidney and some people have even been born without a Kidney and they had a transplanted Kidney put in and they lead normal happy and healthy lives.
Even some people donate one of there Kidney's to someone else that needs a Kidney transplant and those people who've donated one of their Kidney's live normal happy healthy lives as well.