  We define a new differential geometric structure, called Lie rackoid. It
relates to Leibniz algebroids exactly as Lie groupoids relate to Lie
algebroids. Its main ingredient is a selfdistributive product on the manifold
of bisections of a smooth precategory.
  We show that the tangent algebroid of a Lie rackoid is a Leibniz algebroid
and that Lie groupoids gives rise via conjugation to a Lie rackoid. Our main
objective are large classes of examples, including a Lie rackoid integrating
the Dorfman bracket without the cocycle term of the standard Courant algebroid.
