  In a recent paper, Gross and Reeder study arithmetic properties of discrete
Langlands parameters for semi-simple p-adic groups and conjecture that a
special class of these -- the simple wild parameters -- should correspond to
L-packets consisting of simple supercuspidal representations. We provide a
construction of this correspondence and show that the simple wild L-packets
satisfy many expected properties. In particular, they admit a description in
terms of the Langlands dual group and contain a unique generic element for a
fixed Whittaker datum. Moreover, we prove their stability on an open subset of
the regular semi-simple elements, and show that they satisfy a natural
compatibility with respect to unramified base-change.
