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A graph is chordal if every cycle of length at least four has a chord. In1961, Dirac characterized chordal graphs as those graphs that can be built fromcomplete graphs by repeated clique-sums. Generalizing this, we consider theclass of simple $GF(q)$-representable matroids that can be built fromprojective geometries over $GF(q)$ by repeated generalized parallel connectionsacross projective geometries. We show that this class of matroids is closedunder induced minors. We characterize the class by its forbidden inducedminors; the case when $q=2$ is distinctive.

Chordal matroids arising from generalized parallel connections