  We show that the graph $$\Gamma_f=\{(z,f(z))\in{\Bbb C}^2: z\in S\}$$ in
${\Bbb C}^2$ of a function $f$ on the unit circle $S$ which is either
continuous and quasianalytic in the sense of Bernstein or $C^\infty$ and
quasianalytic in the sense of Denjoy is pluripolar.
