Does South Korea allow dual citizenship? (Seoul)

Today I came across a case of a South Korean citizen applying for US citizenship. My question is whether or not the person will loose the South Korean citizenship once becoming a US citizen.
I've read that the South Korean government was working on a project to allow for dual citizenship, amongst other categories, to South Koreans who gained foreign nationality, as long as they agree not to practice overseas rights. Does any of you know if this project has become law? Does South Korea allow for dual citizenship?
Thank you!