We propose a general framework for quantum field theory on the de Sitter space-time (i.e. for local field theories whose truncated Wightman functions are not required to vanish). By requiring that the fields satisfy a weak spectral condition, formulated in terms of the analytic continuation properties of their Wightman functions, we show that a geodesical observer will detect in the corresponding ``vacuum'' a blackbody radiation at temperature $T=1/(2 \pi R)$. We also prove the analogues of the PCT, Reeh-Schlieder and Bisognano-Wichmann theorems.