We have investigated the coherent dynamics of excitonic wave packets i
n In0.135Ga0.865As/GaAs quantum wires with lateral widths between 29 a
nd 85 nm by means of time-integrated degenerate four-wave mixing. In t
he decay of the coherent polarization, we observe periodic modulations
, which we ascribe to quantum beats between the ground state and the f
irst excited state of the heavy-hole exciton In the quantum wires. The
period of these beats decreases with decreasing wire width, indicatin
g an increase of the exciton binding energy due to lateral quantizatio
n. The experimentally observed binding energy rises from 8.7 meV for t
he two-dimensional reference, up to 11.7 meV for the 29-nm-wide quantu
m wires. Detailed calculations of the exciton binding energy for these
structures are in agreement with the experimental data.