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A type-II superconductor is in the "superclean" regime when the spacing hcuo between energy levels in the vortex core greatly exceeds the width of the levels h/r A.key signature of this regime is a fiux-fiow Hall angle 8n that approaches~m/2. We report the first observation of this trend in a high-temperature superconductor.In "60 K" YBa2Cu, 06+, crystals, itan8"i is observed to increase dramatically when the temperature decreases below -40 K, attaining the magnitude 0.85 at 15 K. By extrapolation, we estimate that QUOT increases to 2 -3 at 3 K. Below 40 K, the Hall conductivity 0' y ls negative and decreases as I/H at high fields. PACS numbers: 74.72.Bk, 74.60.6e When a vortex moves in a type-II superconductor, dissipation is produced by the scattering of quasiparticles within the vortex core [1]. The finite lifetime r of quasiparticles trapped in the core leads to a broadening of the energy levels. Usually, the spacing hcoo between the core levels is so much smaller than the widths (QfpT (( 1) that it is a good approximation to treat the core as a column of "normal" material. This picture fails in the opposite limit cdpT » 1. The discrete nature of the levels becomes important, and dissipative processes have to be reconsidered (this is called the "superclean" regime) [2 -5]. In terms of the quasiparticle's mean free path l and the Pippard coherence length g, the superclean condition is equivalent to 1/g » aF/b, (aF is the Fermi energy and 5 the gap parameter). The high-T, superconductors are promising candidates because of the large gap and small aF (5 = 20 -30 meV, aF -500 meV). Recent surface impedance measurements on YBa2Cu307 s (YBCO) indicate that, at 4.2 K, the lifetime is very long in zero field [6 -8], as well as in intense fields (r is estimated to be 2 -6 ps in the core) [9]. The parameter cour is estimated to be -14 in 90K YBCO at temperatures below 15 K, which places YBCO firmly in the superclean regime [9]. The growing evidence notwithstanding, a key signature, namely the distinctive behavior of the Hall effect, has yet to be observed. Microscopic calculations [3,4] predict that tan 8tt in a pure type-II superconductor increases linearly as~coor when &07 )& 1 (8tt is the Hall angle). The vortex velocity u changes from near alignment with J x B towards parallelism with J as pr coincreases (J is the current density and 8 the field). Thus, a Hall angle that diverges towards~m . /2 is an essential piece of evidence for the superclean regime. Up to now, however, the values of 8~observed in YBCO (mostly at temperatures T ) 70 K) have been disappointingly small (i8tt i (0. 05 rad) [10 -12]. Using high-purity "60 K" YBa2Cu 306+y single crystals, we have performed flux-flow measurements down to 11 K. We have uncovered a remarkable increase in 8~that starts near 40 K but shows no sign of saturation at 15 K. The Hall-angle measurements provide direct evidence for the approach to the superclean regime, as well as an estimate of coos-. This is the first demonstration of a diverging Hall angle in a high-T, supe...