We report molecular line observations , made with ASTE and SEST , and dust continuum observations at 0.87 mm , made with APEX , towards the cold dust core G305.136+0.068 . The molecular observations show that the core is isolated and roughly circularly symmetric and imply that it has a mass of 1.1 \times 10 ^ { 3 } M _ { \sun } . A simultaneous model fitting of the spectra observed in four transitions of CS , using a non-LTE radiative transfer code , indicates that the core is centrally condensed , with the density decreasing with radius as r ^ { -1.8 } , and that the turbulent velocity increases towards the center . The dust observations also indicate that the core is highly centrally condensed and that the average column density is 1.1 g cm ^ { -2 } , value slightly above the theoretical threshold required for the formation of high mass stars . A fit to the spectral energy distribution of the emission from the core indicates a dust temperature of 17 \pm 2 K , confirming that the core is cold . Spitzer images show that the core is seen in silhouette from 3.6 to 24.0 \mu m and that is surrounded by an envelope of emission , presumably tracing an externally excited photo-dissociated region . We found two embedded sources within a region of 20″ centered at the peak of the core , one of which is young , has a luminosity of 66 L _ { \sun } and is accreting mass with a high accretion rate , of \sim 1 \times 10 ^ { -4 } M _ { \sun } yr ^ { -1 } . We suggest that this object corresponds to the seed of a high mass protostar still in the process of formation . The present observations support the hypothesis that G305.136+0.068 is a massive and dense cold core in an early stage of evolution , in which the formation of a high mass star has just started .