  We study the feasibility of observing an invisibly decaying Z' at the LHC
through the process pp -> ZZ' -> l+l-XX*, where X is any neutral, (quasi-)
stable particle, whether a Standard Model (SM) neutrino or a new state. The
measurement of the invisible width through this process facilitates both a
model independent measurement of Gamma_{Z' -> \bar{nu} nu} and potentially
detection of light neutral hidden states. Such particles appear in many models
where the Z' is a messenger to a hidden sector, and also if dark matter is
charged under the U(1)' of the Z'. We find that with as few as 30 fb^-1 of data
the invisibly decaying Z' can be observed at 5 sigma over SM background for a 1
TeV Z' with reasonable couplings. If the Z' does not couple to leptons and
therefore cannot be observed in the Drell-Yan channel, this process becomes a
discovery mode. For reasonable hidden sector couplings, masses up to 2 TeV can
be probed at the LHC. If the Z' does couple to leptons, then the rate for this
invisible decay is predicted by on-peak data and the presence of additional
hidden states can be searched for. With 100 fb^-1 of data, the presence of
excess decays to hidden states can be excluded at 95% C.L. if they comprise
20-30% of the total invisible cross section.
