  A quantum theory of the third-harmonic generation in graphene is presented.
An analytical formula for the nonlinear conductivity tensor
$\sigma^{(3)}_{\alpha\beta\gamma\delta}(\omega,\omega,\omega)$ is derived.
Resonant maxima of the third harmonic are shown to exist at low frequencies
$\omega\ll E_F/\hbar$, as well as around the frequency $\omega=2E_F/\hbar$,
where $E_F$ is the Fermi energy in graphene. At the input power of a CO$_2$
laser ($\lambda\approx 10$ $\mu$m) of about 1 MW/cm$^2$ the output power of the
third-harmonic ($\lambda\approx 3.3$ $\mu$m) is expected to be $\simeq 50$
W/cm$^2$.
