This paper explores the feasibility of implementing conventional magnetic recording technology at densities up to one Terabit per square inch. The key limiting physical factor is the superparamagnetic effect (thermal stability) in the recording medium. Ambient thermal energy can cause the magnetic signals to decay. The requirement for thermal stability over periods of years dictates a lower limit to the size of magnetic grains (switching units) in the recording medium. To achieve the highest areal densities, it will be necessary to use a magnetic recording configuration capable of writing and storing data on very small magnetic grains together with a signal processing system capable of recovering data reliably when each bit is recorded on very few such grains. In addition to these physical effects, there are a number of practical engineering factors that must be considered: tolerances on the head geometry, reliability of head-disk interface, track-following accuracy. In an example system, we use a perpendicular recording configuration since it appears to offer some advantage in terms of maximizing the number of stable magnetic grains per unit area. The readback signals are processed by equalization to a simple binary eye followed by soft detection of a low-rate simple parity check code. The example system approaches a density of 1 Terabit per square inch and allows 3 dB of margin against thermal decay, adjacent track interference, etc.