We present a study of the decays B 0 , + → J / ψ π + π − π 0 K 0 , + , using 467 × 10 6 B ¯¯¯ B pairs recorded with the BABAR detector. We present evidence for the decay mode X ( 3872 ) → J / ψ ω , with product branching fractions B ( B + → X ( 3872 ) K + ) × B ( X ( 3872 ) → J / ψ ω ) = [ 0.6 ± 0.2 ( stat ) ± 0.1 ( syst ) ] × 10 − 5 , and B ( B 0 → X ( 3872 ) K 0 ) × B ( X ( 3872 ) → J / ψ ω ) = [ 0.6 ± 0.3 ( stat ) ± 0.1 ( syst ) ] × 10 − 5 . A detailed study of the π + π − π 0 mass distribution from X ( 3872 ) decay favors a negative-parity assignment.