  We study a scalar field on a noncommutative model of spacetime, the fuzzy de
Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$
and its unitary irreducible representations. We solve the Klein-Gordon equation
in $d=2,4$ and show, using a specific choice of coordinates and operator
ordering, that all commutative field modes can be promoted to solutions of the
fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we
specify a Hilbert space representation and study the matrix elements (integral
kernels) of a scalar field: in this way the complete set of solutions of the
fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has
more degrees of freedom than the commutative one, whenever spacetime dimension
is $d>2$. In four dimensions, the new non-geometric, internal modes are
parametrised by $S^2\times W$, where $W$ is a discrete matrix space. Our
results pave the way to analysis of quantum field theory on the fuzzy de~Sitter
space.
