INTEGRAL detected on August 31, 2004, an unusual thermonuclear X-ray burst from the low-mass X-ray binary GX 3+1. Its duration was 30 min, which is between the normal burst durations for this source (⪉10 s) and the superburst observed in 1998 (several hours). We see emission up to 30 keV energy during the first few seconds of the burst where the bolometric peak luminosity approaches the Eddington limit. This peculiar burst is characterized by two distinct phases: an initial short spike of ~6 s consistent with being similar to a normal type I X-ray burst, followed by a remarkable extended decay of cooling emission. We discuss three alternative schemes to explain its twofold nature: 1) unstable burning of a hydrogen/helium layer involving an unusually large amount of hydrogen; 2) pure helium ignition at an unusually large depth (unlikely in the present case); and 3) limited carbon burning at an unusually shallow depth triggered by unstable helium ignition. Though none of these provide a satisfactory description of this uncommon event, the former one seems the most probable.