Ti$_3$C$_2$T$_X$ nano-sheets (MXenes) are an emerging class of two-dimensional materials with outstanding potential to be employed in energy storage, catalysis, and triboelectric applications, on length scales ranging from the nano- to macroscopic. Despite rapidly accelerating interest in this new class of materials, their nanoscale frictional properties and in particular, their potential for solid lubrication on the nanoscale, have not been explored in detail yet. In this short communication, we present the first results on the nanoscale frictional characteristics of MXenes, in the form of a friction map obtained on an isolated Ti$_3$C$_2$T$_x$ nano-sheet deposited on a silicon dioxide substrate via friction force microscopy. Our experiments reveal that few-layer Ti$_3$C$_2$T$_x$ nano-sheets indeed act as solid lubricants on the nanoscale, reducing friction on the silicon dioxide substrates, although not as effectively as few-layer graphene. The results reported here pave the way for further studies focusing on nanoscale solid lubrication achieved by Ti$_3$C$_2$T$_X$ (MXene) nano-sheets.