The study of dynamically cold stellar streams reveals information about the gravitational potential where they reside and provides important constraints on the properties of dark matter. However, the intrinsic faintness of these streams makes their detection beyond Local environments highly challenging. Here, we report the detection of an extremely faint stellar stream (μ_{g, max} = 29.5 mag arcsec⁻²) with an extraordinarily coherent and thin morphology in the Coma Galaxy Cluster. This Giant Coma Stream spans ∼510 kpc in length and appears as a free-floating structure located at a projected distance of 0.8 Mpc from the center of Coma. We do not identify any potential galaxy remnant or core, and the stream structure appears featureless in our data. We interpret the Giant Coma Stream as being a recently accreted, tidally disrupting passive dwarf. Using the Illustris-TNG50 simulation, we identify a case with similar characteristics, showing that, although rare, these types of streams are predicted to exist in Λ-CDM. Our work unveils the presence of free-floating, extremely faint and thin stellar streams in galaxy clusters, widening the environmental context in which these objects are found ahead of their promising future application in the study of the properties of dark matter.