Using the Faint Object Camera (FOC) on the Hubble Space Telescope (HST), we have identified three faint ultraviolet sources in the innermost ~15 arcseconds of the globular cluster NGC 6624. These sources are in addition to the previously discovered UV counterpart to the X-ray source 4U 1820-30, which is observed in the same field. At 1400 A, the sources have dereddened fluxes of 4.4 × 10-16 to 1.8 × 10-15 erg cm-2 s-1 A-1. The faintest source is within the field of view of an existing HST/FOC B image; its B magnitude is ~23.4, or MB ~ 7.8. The two fainter sources may be hot white dwarfs, although it would be unusual to observe two of these objects at such a young age. Alternatively, one or more of the sources could be hot, helium-burning subdwarfs. In particular, the brightest source may be on the extreme blue end of the horizontal branch, which would be notable, as NGC 6624 is a metal-rich cluster with a red horizontal branch. Finally, one or more of these stars could be cataclysmic variables. We briefly discuss future observations that could distinguish among these possibilities.
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