The oxygen isotopic composition has been measured on the constituent phases of Allende inclusion HAL, which has unusual mineralogical, chemical, and calcium isotopic compositions. The oxygen in HAL is heterogeneous, with the rim showing more ''normal'' composition and the hibonite core showing large deviation from both the terrestrial material and the usual inclusions. The observed pattern indicates that HAL is a bona fide and more devious member of the rare ''FUN'' family, whose isotopic composition is characterized by correlated nuclear effects and extreme mass fractionation. The data imply that HAL has suffered a large oxygen mass fractionation of 25%0 per mass unit, followed by exchange with oxygen in a second reservoir. The present experiment supports the identification of two distinct reservoirs from which all refractory inclusions in carbonaceous meteorites derived their oxygen. The required fractionation process seems to operate according to the volatility of various elements and could have been caused by evaporation during a heating event. Nuclear anomalies can be produced in the same heating event if the progenitors of the refractory inclusions were macroscopic aggregates of tiny pre-solar interstellar dust grains and if these grains were destroyed differentially during the evaporation.