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We obtain N = 3 chiral supergravity (SUGRA) compatible with the realitycondition by applying the prescription of constructing the chiral Lagrangiandensity from the usual SUGRA. The $N = 3$ chiral Lagrangian density infirst-order form, which leads to the Ashtekar's canonical formulation, isdetermined so that it reproduces the second-order Lagrangian density of theusual SUGRA especially by adding appropriate four-fermion contact terms. Weshow that the four-fermion contact terms added in the first-order chiralLagrangian density are the non-minimal terms required from the invariance underfirst-order supersymmetry transformations. We also discuss the case of higher Ntheories, especially for N = 4 and N = 8.Comment: 20 pages, Latex, some more discussions and new references added, some  typos corrected, accepted for publication in Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mn /></mml:math>chiral supergravity compatible with the reality condition and higher<i>N</i>chiral Lagrangian density

N=3chiral supergravity compatible with the reality condition and higherNchiral Lagrangian density