Nuclei with magic numbers serve as important benchmarks in nuclear theory. In addition, neutron-rich nuclei play an important role in the astrophysical rapid neutron-capture process (r process). 78Ni is the only doubly magic nucleus that is also an important waiting point in the r process, and serves as a major bottleneck in the synthesis of heavier elements. The half-life of 78Ni has been experimentally deduced for the first time at the Coupled Cyclotron Facility of the National Superconducting Cyclotron Laboratory at Michigan State University, and was found to be 110-60 +100 ms. In the same experiment, a first half-life was deduced for 77Ni of 128 -33+27 ms, and more precise half-lives were deduced for 75Ni and 75Ni of 344 -24-20 ms and 238-18+15 ms, respectively.