  Chondrules are silicate spheroids found in meteorites, serving as important
fossil records of the early solar system. In order to form chondrules,
chondrule precursors must be heated to temperatures much higher than the
typical conditions in the current asteroid belt. One proposed mechanism for
chondrule heating is the passage through bow shocks of highly eccentric
planetesimals in the protoplanetary disk in the early solar system. However, it
is difficult for planetesimals to gain and maintain such high eccentricities.
In this paper, we present a new scenario in which planetesimals in the asteroid
belt region are excited to high eccentricities by the Jovian sweeping secular
resonance in a depleting disk, leading to efficient formation of chondrules. We
study the orbital evolution of planetesimals in the disk using semi-analytic
models and numerical simulations. We investigate the dependence of eccentricity
excitation on the planetesimal's size as well as the physical environment, and
calculate the probability for chondrule formation. We find that 50 - 2000 km
planetesimals can obtain eccentricities larger than 0.6 and cause effective
chondrule heating. Most chondrules form in high velocity shocks, in low density
gas, and in the inner disk. The fraction of chondrule precursors which become
chondrules is about 4 - 9 % between 1.5 - 3 AU. Our model implies that the disk
depletion timescale is $\tau_\mathrm{dep}\approx 1~\mathrm{Myr}$, comparable to
the age spread of chondrules; and that Jupiter formed before chondrules, no
more than 0.7 Myr after the formation of the CAIs.
