  Detecting a deviation from a featureless primordial power spectrum of
fluctuations would give profound insight into the physics of the primordial
Universe. Depending on their nature, primordial features can either provide
direct evidence for the inflation scenario or pin down details of the inflation
model. Thus far, using the cosmic microwave background (CMB) we have only been
able to put stringent constraints on the amplitude of features, but no
significant evidence has been found for such signals. Here we explore the limit
of the experimental reach in constraining such features using 21 cm tomography
at high redshift. A measurement of the 21 cm power spectrum from the Dark Ages
is generally considered as the ideal experiment for early Universe physics,
with potentially access to a large number of modes. We consider three different
categories of theoretically motivated models: the sharp feature models,
resonance models, and standard clock models. We study the improvements on
bounds on features as a function of the total number of observed modes and
identify parameter degeneracies. The detectability depends critically on the
amplitude, frequency and scale-location of the features, as well as the angular
and redshift resolution of the experiment. We quantify these effects by
considering different fiducial models. Our forecast shows that a cosmic
variance limited 21 cm experiment measuring fluctuations in the redshift range
$30\leq z \leq 100$ with a 0.01-MHz bandwidth and sub-arcminute angular
resolution could potentially improve bounds by several orders of magnitude for
most features compared to current Planck bounds. At the same time, 21 cm
tomography also opens up a unique window into features that are located on very
small scales.
