We present an entropy-stable (ES) Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the single-fluid magneto-hydrodynamics equations with a generalized Lagrange multiplier divergence cleaning mechanism (GLM-MHD). Traditionally, ES DG discretizations have used a nodal collocated variant of the DG method known as the DG spectral element method (DGSEM) on Legendre-Gauss-Lobatto (LGL) points. For instance, the ES LGL-DGSEM discretization of the GLM-MHD system was presented in [1,2]. Recently, Chan et al. [3] presented an ES DGSEM scheme that uses Legendre-Gauss (LG) points instead of LGL for conservation laws. Because of the enhanced accuracy of the LG quadrature, the ES LG-DGSEM is more accurate than its LGL counterpart for conservation laws. Unfortunately, this discretization scheme cannot be applied directly to the GLM-MHD system, which requires non-conservative terms for the continuous entropy analysis to hold and to ensure Galilean invariance for the divergence cleaning technique. We derive a novel strategy to discretize the non-conservative terms of the GLM-MHD system that achieves entropy conservation/stability with the LG quadrature. Moreover, this novel discretization strategy allows us to reformulate the ES LGL-DGSEM discretization of the GLM-MHD equations [1] in a compact manner. We provide a numerical verification of the entropy behavior and convergence properties of our novel scheme on 3D curvilinear meshes. Moreover, we test the robustness and accuracy of our scheme with under-resolved MHD turbulence simulations. The numerical experiments suggest that the ES LG-DGSEM for the GLM-MHD system is more accurate and robust than its LGL counterpart. References [1] Bohm, M., Winters, A. R., Gassner, G. J., Derigs, D., Hindenlang, F., & Saur, J. (2020). An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification. Journal of Computational Physics, 422, 108076. [2] Rueda-Ramírez, A. M., Hennemann, S., Hindenlang, F. J., Winters, A. R., & Gassner, G. J. (2021). An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. Journal of Computational Physics, 444, 110580. [3] Chan, J., Del Rey Fernández, D. C., & Carpenter, M. H. (2019). Efficient entropy stable Gauss collocation methods. SIAM Journal on Scientific Computing, 41(5), A2938-A2966.