  Chiral polymers are ubiquitous in nature and in the cellular context they are
often found in association with membranes. Here we show that surface bound
polymers with an intrinsic twist and anisotropic bending stiffness can exhibit
a sharp continuous phase transition between states with very different
effective persistence lengths as the binding affinity is increased. Above a
critical value for the binding strength, determined solely by the torsional
modulus and intrinsic twist rate, the filament can exist in a zero twist,
surface bound state with a homogeneous stiffness. Below the critical binding
strength, twist walls proliferate and function as weak or floppy joints that
sharply reduce the effective persistence length that is measurable on long
lengthscales. The existence of such dramatically different conformational
states has implications for both biopolymer function {\it in vivo} and for
experimental observations of such filaments {\it in vitro}.
