Yes of course, it is possible to live with just one kidney. People with one kidney live a healthy and normal life. In fact, there are many people in our world today, living with just one functioning kidney.
It is possible to be born with one kidney. A person may have donated one kidney to a person who needed a kidney transplant. A person may have had one kidney removed as a result of an injury or cancer.
A person with one kidney can live essentially the same as those with two kidneys. This is because the remaining kidney has the ability to compensate for its missing counterpart.