  We show that stringent limits on leptoquarks that couple to first-generation
quarks and left-handed electrons or muons can be derived from the spectral
shape of the charged-current Drell-Yan process ($p p \to \ell^\pm \nu$) at Run
2 of the LHC. We identify and examine all six leptoquark species that can
generate such a monolepton signal, including both scalar and vector
leptoquarks, and find cases where the leptoquark exchange interferes
constructively, destructively or not at all with the Standard Model signal.
When combined with the corresponding leptoquark-mediated neutral-current ($p p
\to \ell^+ \ell^-$) process, we find the most stringent limits obtained to
date, outperforming bounds from pair production and atomic parity violation. We
show that, with 3000 fb$^{-1}$ of data, combined measurements of the transverse
mass in $p p \to \ell^\pm \nu$ events and invariant mass in $p p \to \ell^+
\ell^-$ events can probe masses between 8 TeV and 18 TeV, depending on the
species of leptoquark, for electroweak-sized couplings. In light of such robust
sensitivities, we strongly encourage the LHC experiments to interpret Drell-Yan
(dilepton and monolepton) events in terms of leptoquarks, alongside usual
scenarios like $Z'$ bosons and contact interactions.
