Heat-assisted magnetic recording (HAMR) is being developed as the next-generation magnetic recording technology. Critical aspects of this technology, such as plasmonic near-field transducer (NFT) and high anisotropy granular FePt media, have been demonstrated and reported. However, progress with areal density was limited until recently. In this paper, we report a basic technology demonstration (BTD) of HAMR, at 1.007 Tbpsi with a linear density of 1975 kBPI and track density of 510 kTPI, resulting from advances in magnetic recording heads with NFT and FePtX media. This demonstration not only shows significant areal density improvement over previously reported HAMR demos, more significantly, it shows HAMR recording at a much higher linear density compared to previous reports. It is an important milestone for the development of such a new technology. Many challenges still remain to bring this technology to market, such as system reliability and further advancement of areal density.