  Different inflationary models predict oscillatory features in the primordial
power spectrum. These can leave an imprint on both the cosmic microwave
background (CMB) and the large-scale structure (LSS) of our Universe, that can
be searched for with current data. Inspired by the axion-monodromy model of
inflation, we search for primordial oscillations that are logarithmic in
wavenumber, using both CMB data from the Planck satellite and LSS data from the
WiggleZ galaxy survey. We find that, within our search range for the new
oscillation parameters (amplitude, frequency and phase), both CMB-only and
CMB+LSS data yield the same best-fit oscillation frequency of
$\log_{10}\omega=1.5$, improving the fit over $\Lambda$CDM by $\Delta\chi^2\!
=\! -9$ and $\Delta\chi^2\! =\! -13$ (roughly corresponding to $2\sigma$ and
$2.8\sigma$ significance), respectively. Bayesian evidence for the
log-oscillation model versus $\Lambda$CDM indicates a very slight preference
for the latter. Future CMB and LSS data will further probe this scenario.
