We offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). Given a rig category R we construct a natural additive group completion (R) over bar that retains the multiplicative structure, hence has become a ring category. If we start with a commutative rig category R (also known as a symmetric bimonoidal category), the additive group completion (R) over bar will be a commutative ring category. In an accompanying paper we show how to use this construction to prove the conjecture that the algebraic K-theory of the connective topological K-theory ring spectrum ku is equivalent to the algebraic K-theory of the rig category V of complex vector spaces.