  There exists some tension on large scales between the Planck data and the
LCDM concordance model of the Universe, which has been amplified by the
recently claimed discovery of non-zero tensor to scalar ratio $r$. At the same
time, the current best-fit value of $r$ suggests large field inflation delta
phi>M_p, which requires a UV complete description of inflation. A very
promising working example that predicts large tensor modes and can be UV
completed is axion monodromy inflation. This realization of inflation naturally
produces oscillating features, as consequence of a broken shift symmetry. We
analyse a combination of Planck, ACT, SPT, WMAP low l polarization and BICEP2
data, and show a long wavelength feature from a periodic potential can
alleviate the tension at low multipoles with an improvement delta chi^2 ~2.5-4
per degree of freedom, depending on the level of foreground subtraction. As
with an introduction of running, one expects that any scale dependence should
lead to a worsened fit at high multipoles. We show that the logarithmic nature
of the axion feature in combination with a tilt n_s~1 allows the fit to be
identical to a no feature model at the 2 percent level on scales 100 =< l
=<3500, and quite remarkable actually slightly improves the fit at scales l
>2000. We also consider possible unremoved dust foregrounds and show that
including these hardly changes the best-fit parameters. Our analysis suggests
an axion decay constant of f/M_p ~O(.01). We discuss how Planck measurements of
the TE and EE spectra can further constrain axion monodromy inflation with such
a large feature. A measurement of the large scale structure power spectrum is
even more promising, as the effect is much bigger since the tensor modes do not
affect the large scales. At the same time, a feature could also lead to a lower
sigma8, lifting the tension between CMB and SZ constraints on sigma8.
