Absorption spectra of conjugated polymer chains (polydiacetylene) diluted in transparent single crystals of the precursor monomer 3BCMU are presented. The exciton states of the conjugated chains make a transition to a nonabsorbing polariton state once the polymer concentration eta exceeds 10(-4) in weight. This transition to persistent coherent coupling of exciton and light is attributed to a large transition dipole moment per repeat unit and the long range coherence of pi bonds. It leads to saturated absorbance over a spectral range that increases with eta and includes finally most of the pi-pi(*) transitions. The transmission in the saturated state is 1%-3% below 100 K and almost independent of sample thickness and polymer content. This indicates that absorption occurs in a surface region which shrinks with polymer content while energy dissipation within the sample is reduced for the coherently coupled state of exciton and photon. The polariton state is weakly coupled to light of perpendicular polarization by higher electric moments of the exciton which generate sharp spectral features of excess absorption on top of the saturated absorbance.