  In this paper we construct a connection on the trivial G-bundle on the
projective line for any simple complex algebraic group G, which is regular
outside of the points 0 and infinity, has a regular singularity at the point 0,
with principal unipotent monodromy, and has an irregular singularity at the
point infinity, with slope 1/h, the reciprocal of the Coxeter number of G. This
connection, which admits the structure of an oper in the sense of Beilinson and
Drinfeld, appears to be the characteristic 0 counterpart of a hypothetical
family of l-adic representations, which should parametrize a specific
automorphic representation under the global Langlands correspondence. These
l-adic representations, and their characteristic 0 counterparts, have been
constructed in some cases by Deligne and Katz. Our connection is constructed
uniformly for any simple algebraic group, and characterized using the formalism
of opers. It provides an example of the geometric Langlands correspondence with
wild ramification. We compute the de Rham cohomology of our connection with
values in representations of G, and describe its differential Galois group as a
subgroup of G.
