The progresses in the micropulling-down technique allow heavy scintillating crystals to be grown directly into a fibre geometry of variable shape, length and diameter. Examples of materials that can be grown with this technique are Lutetium Aluminum Garnets (LuAG, Lu sub(3)Al sub(5)O sub(12)) and Yttrium Aluminum Garnets (YAG, Y sub(3)Al sub(5)O sub(12)). Thanks to the flexibility of this approach, combined with the high density and good radiation hardness of the materials, such a technology represents a powerful tool for the development of future calorimeters. As an important proof of concept of the application of crystal fibres in future experiments, a small calorimeter prototype was built and tested on beam. A grooved brass absorber (dimensions 26cmx7cmx16cm) was instrumented with 64 LuAG fibres, 56 of which were doped with Cerium, while the remaining 8 were undoped. Each fibre was readout individually using 8 eightfold Silicon Photomultiplier arrays, thus providing a highly granular description of the shower development inside the module as well as good tracking capabilities. The module was tested at the Fermilab Test Beam Facility using electrons and pions in the 2-16 GeV energy range. The module performance as well as fibre characterization results from this beam test are presented.