  Despite the growing number of confident binary black hole coalescences
observed through gravitational waves so far, the astrophysical origin of these
binaries remains uncertain. Orbital eccentricity is one of the clearest tracers
of binary formation channels. Identifying binary eccentricity, however, remains
challenging due to the limited availability of gravitational waveforms that
include effects of eccentricity. Here, we present observational results for a
waveform-independent search sensitive to eccentric black hole coalescences,
covering the third observing run (O3) of the LIGO and Virgo detectors. We
identified no new high-significance candidates beyond those that were already
identified with searches focusing on quasi-circular binaries. We determine the
sensitivity of our search to high-mass (total mass $M>70$ $M_\odot$) binaries
covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to
compare model predictions to search results. Assuming all detections are indeed
quasi-circular, for our fiducial population model, we place an upper limit for
the merger rate density of high-mass binaries with eccentricities $0 < e \leq
0.3$ at $0.33$ Gpc$^{-3}$ yr$^{-1}$ at 90\% confidence level.
