In　this　paper,　we　study　the　time-asymptotically　nonlinear　stability　of　rarefaction　waves　for　the　Cauchy　problem　of　the　compressible　Navier-Stokes　equations　for　a　reacting　mixture　with　zero　heat　conductivity　in　one　dimension.　If　the　corresponding　Riemann　problem　for　the　compressible　Euler　system　admits　the　solutions　consisting　of　rarefaction　waves　only,　it　is　shown　that　its　Cauchy　problem　has　a　unique　global　solution　which　tends　time-asymptotically　towards　the　rarefaction　waves,　while　the　initial　perturbation　and　the　strength　of　rarefaction　waves　are　suitably　small.