We propose a new notion of multiplicative connection in the tangent bundle of a Lie groupoid. Multiplicative connections are a global version of Q-connections on a Q-manifold and their existence is obstructed by a cohomology class which a global counterpart of the Atiyah class of a Q-manifold (in the sense of Mehta, Stiénon and Xu). We discuss the Lie theory of multiplicative connections and present a bunch of examples. Our results can be easily generalized to multiplicative connections in VB-groupoids. This is the first step towards a theory of linear connections on differentiable stacks (joint work with: F. Pugliese and G. Sparano).