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Abstract. In this paper we offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). More precisely, given a rig category R we construct a natural additive group completionR of R that retains the multiplicative structure, meaning that it remains a rig category. In other words, it has become a ring category. If we start with a commutative rig category R (also known as a symmetric bimonoidal category), the additive group completionR can be taken to be a commutative rig category. In an accompanying paper we show how this can be used to prove the conjecture from [BDR] that K(ku) is the K-theory of the rig category of complex vector spaces.