In this article we present a new C ^* -algebraic deformation of the Lorentz group. It is obtained by means of the Rieffel deformation applied to \mathrm{SL}(2,ℂ) . We give a detailed description of the resulting quantum group \mathbb{G} = (A,Δ) in terms of generators \hat α, \hat β, \hat γ, \hat δ \in A^η – the quantum counterparts of the matrix coefficients α, β, γ, δ of the fundamental representation of \mathrm{SL}(2,ℂ) . In order to construct \hat β – the most involved of the four generators – we first define it on the quantum Borel subgroup \mathbb G_0\subset\mathbb G , then on the quantum complement of the Borel subgroup and finally we perform the gluing procedure. In order to classify representations of the C {}^* -algebra A and to analyze the action of the comultiplication Δ on the generators \hat α, \hat β, \hat γ, \hat δ we employ the duality in the theory of locally compact quantum groups.