  In this paper we introduce a class of hypergraphs that we call chordal. We
also extend the definition of triangulated hypergraphs, given in \cite{VT}, so
that a triangulated hypergraph, according to our definition, is a natural
generalization of a chordal (rigid circuit) graph. In \cite{F1}, Fr\"oberg
shows that the chordal graphs corresponds to graph algebras, $R/I(\mc{G})$,
with linear resolutions. We extend Fr\"oberg's method and show that the
hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs
that includes the chordal hypergraphs, have linear resolutions. The definitions
we give, yield a natural higher dimensional version of the well known flag
property of simplicial complexes. We obtain what we call $d$-flag complexes.
