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Let $\Gamma$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). Weshow that if the trace field of $\Gamma$ is contained in $\mathbb R$, $\Gamma$preserves a totally geodesic submanifold of constant negative sectionalcurvature. Furthermore if $\Gamma$ is irreducible, $\Gamma$ is a Zariski denseirreducible discrete subgroup of SO(n,1) up to conjugation. This is an analogof a theorem of Maskit for general semisimple Lie groups of rank $1$.

Complex and Quaternionic hyperbolic Kleinian groups with real trace fields