A novel hexagonal phase discovered near the Ca15Au60Sn25 quasicrystal and its cubic approximants (ACs) was synthesized by means of high-temperature solid-state reactions. Single-crystal structural analyses show that this is a Gd14Ag51 isotype with composition within the range Ca14Au45.56(4)−46.67(4)Sn5.14(3)−4.14(3), space group P6/m (No. 175), and lattice parameters a = 12.763(3)−12.879(3) Å and c = 9.326(3)−9.3815(4) Å. In this phase, Sn mixes with Au in two of seven anionic sites to give a strong coloring that generates a narrow honeycomb-like Au/Sn template, in which sizable columns of hexagonal Au stars are confined. This phase transforms into the cubic 2/1 AC phase through a peritectic reaction at ∼678 °C. The valence electron count per atom (e/a) of the present phase is in the range 1.41−1.45. However, it does not appear to follow a Hume−Rothery mechanism.