The concept of doing coins across at chest height, from the fingertips of one hand to the fingertips of the other, is generally known today as “Three Fly”. This is due to Chris Kenner's popular handling, detailed in his booklet of the same name, Three Fly, 1991. He also published handlings in Magic Man Examiner, No. 2, 1991, p. 2, and in Totally Out of Control, 1992, p. 69. The concept itself, however, predates Kenner by almost a hundred years.
W.H.J. Shaw describes the plot in Magic Up to Date; or, Shaw's Magical Instructor, 1896, p. 59. By today's nomenclature, Shaw's trick could be called “Twenty Fly”. In it, the magician causes a coin to appear at the fingertips of the left hand, where it is then caused to travel invisibly to the right fingertips. This is repeated nineteen more times, with each new coin forming a larger and larger fan of coins in the right hand. This trick, titled “The Ne Plus Ultra Coin Trick”, must not have garnered much attention as it doesn't seem to have been described anywhere else (a marketed trick appeared under the same name several years later, but is unrelated to Shaw's; see the ad in Mahatma, Vol. 7 No. 2, Aug. 1903, p. 20).
The plot enjoyed a renaissance in the late 1980s and early 1990s. According to Jonathan Townsend, he showed his fingertip coins across handling to Chris Kenner and Bob Kohler in 1987, at which point both men developed their own handlings. The plot went viral from there. This account can be found—along with Jonathan's original handling—in Genii, Vol. 69 No. 9, Sep. 2006, p. 30. Curtis Kam notes, however, that Michael Ammar describes a pre-Townsend fingertip-to-fingertip transportation as a solution to the oft-pondered problem of how to make the final coin of a coins across routine climactic; see Ammar's The Topit Book, 1983, p. 67.
Apart from Kenner's handling already mentioned, other notable versions from the period include the middle portion of Gary Kurtz's “Trio” from Unexplainable Acts, 1990, p. 67, and Troy Hooser's handlings that eventually saw print in DesTROYers, 1999, pp. 37 & 75.