  The H1 Collaboration reports the first measurement of the 1-jettiness event
shape observable $\tau_1^b$ in neutral-current deep-inelastic electron-proton
scattering (DIS). The observable $\tau_1^b$ is equivalent to a thrust
observable defined in the Breit frame. The data sample was collected at the
HERA $ep$ collider in the years 2003-2007 with center-of-mass energy of
$\sqrt{s}=319\,\text{GeV}$, corresponding to an integrated luminosity of
$351.1\,\text{pb}^{-1}$. Triple differential cross sections are provided as a
function of $\tau_1^b$, event virtuality $Q^2$, and inelasticity $y$, in the
kinematic region $Q^2>150\,\text{GeV}^{2}$. Single differential cross section
are provided as a function of $\tau_1^b$ in a limited kinematic range. Double
differential cross sections are measured, in contrast, integrated over
$\tau_1^b$ and represent the inclusive neutral-current DIS cross section
measured as a function of $Q^2$ and $y$. The data are compared to a variety of
predictions and include classical and modern Monte Carlo event generators,
predictions in fixed-order perturbative QCD where calculations up to
$\mathcal{O}(\alpha_s^3)$ are available for $\tau_1^b$ or inclusive DIS, and
resummed predictions at next-to-leading logarithmic accuracy matched to fixed
order predictions at $\mathcal{O}(\alpha_s^2)$. These comparisons reveal
sensitivity of the 1-jettiness observable to QCD parton shower and resummation
effects, as well as the modeling of hadronization and fragmentation. Within
their range of validity, the fixed-order predictions provide a good description
of the data. Monte Carlo event generators are predictive over the full measured
range and hence their underlying models and parameters can be constrained by
comparing to the presented data.
