We report a measurement of the lifetime of the
Ω
0
c
baryon using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of
3.0
 
 
fb
−
1
collected by the LHCb experiment. The sample consists of about
1000
 
 
Ω
−
b
→
Ω
0
c
μ
−
¯
ν
μ
X
signal decays, where the
Ω
0
c
baryon is detected in the
p
K
−
K
−
π
+
final state and
X
represents possible additional undetected particles in the decay. The
Ω
0
c
lifetime is measured to be
τ
Ω
0
c
=
268
±
24
±
10
±
2
 
 
fs
, where the uncertainties are statistical, systematic, and from the uncertainty in the
D
+
lifetime, respectively. This value is nearly four times larger than, and inconsistent with, the current world-average value.