  We define the spherical Hecke algebra H for an almost split Kac-Moody group G
over a local non-archimedean field. We use the hovel I associated to this
situation, which is the analogue of the Bruhat-Tits building for a reductive
group. The stabilizer K of a special point on the standard apartment plays the
role of a maximal open compact subgroup. We can define H as the algebra of
K-bi-invariant functions on G with almost finite support. As two points in the
hovel are not always in a same apartment, this support has to be in some large
subsemigroup G+ of G. We prove that the structure constants of H are
polynomials in the cardinality of the residue field, with integer coefficients
depending on the geometry of the standard apartment. We also prove the Satake
isomorphism between H and the algebra of Weyl invariant elements in some
completion of a Laurent polynomial algebra. In particular, H is always
commutative. Actually, our results apply to abstract "locally finite" hovels,
so that we can define the spherical algebra with unequal parameters.
