  We show that a molecular junction can give large values of the thermoelectric
figure of merit $ZT$, and so could be used as a solid state energy conversion
device that operates close to the Carnot efficiency. The mechanism is similar
to the Mahan-Sofo model for bulk thermoelectrics -- the Lorenz number goes to
zero violating the Wiedemann-Franz law while the thermopower remains non-zero.
The molecular state through which charge is transported must be weakly coupled
to the leads, and the energy level of the state must be of order $k_B T$ away
from the Fermi energy of the leads. In practice, the figure of merit is limited
by the phonon thermal conductance; we show that the largest possible
$ZT\sim(\tilde{G}_{th}^{ph})^{-1/2}$, where $\tilde{G}_{th}^{ph}$ is the phonon
thermal conductance divided by the thermal conductance quantum.
