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Context: Core accretion models of massive star formation require the existence of massive, starless cores within molecular clouds. Yet, only a small number of candidates for such truly massive, monolithic cores are currently known. Aims: Here we analyse a massive core in the well-studied infrared-dark cloud (IRDC) called the 'dragon cloud' (also known as G028.37+00.07 or 'Cloud C'). This core (C2c1) sits at the end of a chain of a roughly equally spaced actively star-forming cores near the centre of the IRDC. Methods: We present new high-angular resolution 1 mm ALMA dust continuum and molecular line observations of the massive core. Results: The high-angular resolution observations show that this region fragments into two cores C2c1a and C2c1b, which retain significant background-subtracted masses of 23 Msun and 2 Msun (31 Msun and 6 Msun without background subtraction), respectively. The cores do not appear to fragment further on the scales of our highest angular resolution images (0.200 arcsec, 0.005 pc ~ 1000 AU). We find that these cores are very dense (nH2 > 10^6 cm-3) and have only trans-sonic non-thermal motions (Ms ~ 1). Together the mass, density and internal motions imply a virial parameter of < 1, which suggests the cores are gravitationally unstable, unless supported by strong magnetic fields with strengths of ~ 1 - 10 mG. From CO line observations, we find that there is tentative evidence for a weak molecular outflow towards the lower-mass core, and yet the more massive core remains devoid of any star formation indicators. Conclusions: We present evidence for the existence of a massive, pre-stellar core, which has implications for theories of massive star formation. This source warrants follow-up higher-angular-resolution observations to further assess its monolithic and pre-stellar nature.