Talos I was the first planet in the Talosian planetary system. This small planet was located over one astronomical unit from the binary stars Talos A and Talos B. (TOS: "The Cage", "The Menagerie, Part I")
Background
The planet was never mentioned in dialog; this name came from a map of the Talosian system.
"The Explored Galaxy"
This chart was first seen, chronologically, in 2293. (Star Trek VI: The Undiscovered Country) This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
Star Trek: Star Charts
Talos I was classified as a B-class planet. In 2378, Talos I was located in or near Federation space, in the Alpha Quadrant. (Pgs. 40-41, "United Federation of Planets III")