We report on the first experimental observation of a current-driven instability developing in a quasineutral matter-antimatter beam. Strong magnetic fields (amp;gt;= 1 T) are measured, via means of a proton radiography technique, after the propagation of a neutral electron-positron beam through a background electron-ion plasma. The experimentally determined equipartition parameter of epsilon(B) approximate to 10(-3) is typical of values inferred from models of astrophysical gamma-ray bursts, in which the relativistic flows are also expected to be pair dominated. The data, supported by particle-in-cell simulations and simple analytical estimates, indicate that these magnetic fields persist in the background plasma for thousands of inverse plasma frequencies. The existence of such long-lived magnetic fields can be related to analog astrophysical systems, such as those prevalent in lepton-dominated jets.Funding Agencies|EPSRC [EP/N022696/1, EP/N027175/1, EP/L013975/1, EP/N002644/1, EP/P010059/1]; DOE [DE-NA0002372]; ARO [W911NF-16-1-0044]