  Topological insulators supporting non-abelian anyonic excitations are at the
center of attention as candidates for topological quantum computation. In this
paper, we analyze the ground-state properties of disordered non-abelian anyonic
chains. The resemblance of fusion rules of non-abelian anyons and real space
decimation strongly suggests that disordered chains of such anyons generically
exhibit infinite-randomness phases. Concentrating on the disordered golden
chain model with nearest-neighbor coupling, we show that Fibonacci anyons with
the fusion rule $\tau\otimes\tau={\bf 1}\oplus \tau$ exhibit two
infinite-randomness phases: a random-singlet phase when all bonds prefer the
trivial fusion channel, and a mixed phase which occurs whenever a finite
density of bonds prefers the $\tau$ fusion channel. Real space RG analysis
shows that the random-singlet fixed point is unstable to the mixed fixed point.
By analyzing the entanglement entropy of the mixed phase, we find its effective
central charge, and find that it increases along the RG flow from the random
singlet point, thus ruling out a c-theorem for the effective central charge.
