Vector Galileons are vector fields that have scalar Galileons as their longitudinal modes. They belong to a general, nonlinear, higher derivative extension of the Proca system. Due to this close relation with scalar Galileons, the covariant theories possess interesting cosmological applications such as self-acceleration and the ability to screen via a Vainshtein mechanism. Such properties lends support to these theories forming an alternative explanation for the late time cosmic expansion. I will introduce a nonlinear, higher derivative extension to the Higgs mechanism that generates vector Galleons spontaneously. I will further discuss how the covariantisation of this model is made nontrivial due to the presence of higher derivatives and how it can be achieved via the use of non-minimal derivative couplings with curvature tensors. We find that the covariant theory can be seen as a higher order extension to Higgs G-inflation and therefore the range of possible cosmological applications is extended beyond the late time cosmic expansion of scalar and vector Galileons to include early universe physics.