The Rachelis system was a densely-populated star system in Federation space. Science Station Tango Sierra, a medical research outpost, was located in this system.

The system was struck by an outbreak of a new strain of plasma plague in 2365. To combat the disease, specimens of plasma plague were transported from 'aucdet IX to Science Station Tango Sierra by the USS Enterprise-D. (TNG: "The Child")

"Ra-CHEL-is" was the pronunciation for this system from the script pronunciation guide. [1]
According to Star Trek: Star Charts (p. 66) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Science Station Tango Sierra, and by extension the Rachelis system, was located in the Beta Quadrant.