  The dark matter may be a composite particle that is accessible via a weakly
coupled portal. If these hidden-sector states are produced at the Large Hadron
Collider (LHC), they would undergo a QCD-like shower. This would result in a
spray of stable invisible dark matter along with unstable states that decay
back to the Standard Model. Such "semi-visible" jets arise, for example, when
their production and decay are driven by a leptophobic $Z'$ resonance; the
resulting signature is characterized by significant missing energy aligned
along the direction of one of the jets. These events are vetoed by the current
suite of searches employed by the LHC, resulting in low acceptance. This Letter
will demonstrate that the transverse mass---computed using the final-state jets
and the missing energy---provides a powerful discriminator between the signal
and the QCD background. Assuming that the $Z'$ couples to the Standard Model
quarks with the same strength as the $Z^0$, the proposed search can discover
(exclude) $Z'$ masses up to 2.5 TeV (3.5 TeV) with 100 fb$^{-1}$ of 14 TeV data
at the LHC.
