  We present a Fefferman-type construction from Lagrangian contact to conformal
structures and examine several related topics. In particular, we concentrate on
describing the canonical curves and their correspondence. We show that chains
and null-chains of an integrable Lagrangian contact structure are the
projections of null-geodesics of the Fefferman space. Employing the Fermat
principle, we realize chains as geodesics of Kropina (pseudo-Finsler) metrics.
Using recent rigidity results, we show that ``sufficiently many'' chains
determine the Lagrangian contact structure. Separately, we comment on
Lagrangian contact structures induced by projective structures and the special
case of dimension three.
