  We define the Furstenberg boundary of a locally compact Hausdorff \'etale
groupoid, generalising the Furstenberg boundary for discrete groups, by
providing a construction of a groupoid-equivariant injective envelope. Using
this injective envelope, we establish the absence of recurrent amenable
subgroups in the isotropy as a sufficient criterion for the intersection
property of a locally compact Hausdorff \'etale groupoid with compact unit
space and no fixed points. This yields a criterion for C*-simplicity of minimal
groupoids.
