Ther is nothing incompatible about modes and chords. Modes refer to the notes of the melody, the chords are the harmonies you put with the melody. You can write a modal tune without any harmonic implications at all (most eastern music, and a lot of archaic British and Irish music); but you can write an equally modal tune(like Drunken Sailor or Soldiers Joy) which is based on arpeggiated chords. both kinds of music are equally modal: one is harmonic, one isnt.