An extreme scattering event (ESE) has been detected in the direction of the millisecond pulsar J1643-1224 at 1.28 and 1.41 GHz. Its duration is 3 years and this makes it the longest ESE ever recorded. We have used the standard model of a purely refractive lens to interpret the observed radio light curves. This lens is a fully ionized cloud crossing the line of sight. We have found that our data imply that its transverse size is 56 AU, which is much larger than ~1 AU typical of the other ESEs in the direction of the pulsar B1937+21. If the cloud is located at the mid-distance to J1643-1224 (2500 pc), its electron density is 130 e cm-3. Such a highly pressurized structure has a short lifetime (29 yr), and this requires a replenishment mechanism at work in the interstellar medium that is unidentified at present. Alternative models are filamentary clouds seen through their long axis or a cold molecular hydrogen cloud with an ionized shell, as proposed by Walker & Wardle.