Chebyshev quadrature for measures with a strong singularity

We give examples of measures admitting Chebyshev quadrature that have a singular behavior near one end point. In our main result we present such a measure on [0,1] whose density behaves like t−1(logt)−2 as t → 0. These examples are derived from results of He and Saff (1994) on the zeros of Faber polynomials associated with an m-cusped hypocycloid. We also give a formula for the asymptotic distribution of these zeros.