Observations of the Earth as a planet using the earthshine technique (i.e. looking at the light reflected from the dark side of the Moon) have been used for climate and astrobiology studies. They provide information about the planetary albedo, a fundamental parameter of the Earth's energy balance. Here we present, for the first time, observations of the earthshine taken at high spectral resolution. The high spectral resolution was chosen in order to investigate the possibility of detecting metallic layers in the Earth's atmosphere of geological or meteoritic origin. The Spettrografo Alta Risoluzione Galileo echelle spectrograph at the Telescopio Nazionale Galileo in La Palma was used to acquire the earthshine data. Observations were carried out on several nights in 2011 February, with the spectral resolution set at 29 000, covering a spectral range from the near-ultraviolet (360 nm) to near-infrared (1011.9 nm). While we find evidence for the detection of a Na layer in the earthshine, other atomic species are not detected, perhaps due to the low signal-to-noise ratio of the observations and the difficult telluric corrections. The Na layer is found to vary between observation dates, which we speculate is due to physical variations in mesospheric Na concentrations.