Blade dancer triggered ability defy is it still trigger?

Yes — Blade Dancer's trigger still resolves even if the spell that "chose" the unit is countered by Defy.

Targets are chosen at finalization, which happens before the caster passes priority and before Defy can even be played. Blade Dancer's triggered ability is already on the chain at that point, and Defy only removes the spell — it doesn't touch the already-triggered ability (FAQ #6256). This assumes the spell's effect has you doing the choosing; automatic effects that select a unit for you (like Back-Alley Bar) don't trigger Blade Dancer at all.