A high-precision Penning trap mass measurement of the exotic 8He nuclide (T(1/2)=119 ms) has been carried out resulting in a reduction of the uncertainty of the halo binding energy by over an order of magnitude. The new mass, determined with a relative uncertainty of 9.2 x 10(-8) (deltam=690 eV) is 13 keV less bound than the previously accepted value. The mass measurement is of great relevance for the recent charge-radius measurement of 8He [P. Mueller, Phys. Rev. Lett. 99, 252501 (2007).10.1103/PhysRevLett.99.252501]. The 8He mass is the first result from the newly-commissioned Penning trap: TITAN (TRIUMF's Ion Trap for Atomic and Nuclear science) at the ISAC (Isotope Separator and Accelerator) radioactive beam facility at TRIUMF.