We propose a low order discontinuous Galerkin method for in- compressible flows. Stability of the discretization of the Laplace operator is obtained by enriching the space element wise with a non-conforming quadratic bubble. This enriched space allows for a wider range of pressure spaces. We prove optimal convergence estimates and local conservation of both mass and linear momentum independent of numerical parameters. Discontinuous Galerkin (DG) methods for incompressible flow has been studied in Hansbo and Larson (9) in the framework of Nitsche's method and inf-sup stable velocity pressure pairs. The analysis was extended by Toselli to the hp-framework using mixed or equal order stabilized formulations in (12). Local discontinuous Galerkin methods with equal order velocity and pressure spaces stabilized using penalty on the interelement pressure jumps was proposed by Cockburn et al. (6). The Navier-Stokes equations discretized using DG has recently been given a full analysis in the framework of domain decomposition on non-matching meshes using DG techniques by Girault et al. (8). In this paper we extend our previous work on low order discontinuous Galerkin methods for scalar second order elliptic problems to the case of incompressible flow problems (2, 3). Using piecewise a!ne d iscontinuous finite elements enriched with non-conforming bubbles we can eliminate all stabilization terms from the formulation without compromising the adjoint consistency. The upshot is that linear momentum is conserved locally and optimal convergence in the L2-norm may be proven using a duality argument. This is a consequence of the fact that the vectors of the velocity gradient matrix are functions in the lowest order Raviart- Thomas space for our choice of velocity finite element space (see also (1)). Several choices for the pressure space are possible without introducing a penalty term. Indeed we can use either globally continuous, piecewise a!ne functions, piecewise constant, discontinuous functions or functions from a direct sum of these two sets of functions and still satisfy the inf-sup condition uniformly with respect to the mesh size. Depending on the choice of pressure space slightly di"erent results may be ob- tained. When the pressure space consists of continuous functions we prove that the stresses are continuous. Using spaces with discontinuous functions for the pressure on the other hand leads to a method that also enjoys local mass conservation and