We present the discovery of a binary millisecond pulsar (MSP), PSR J2322$-$2650, found in the Southern section of the High Time Resolution Universe survey. This system contains a 3.5-ms pulsar with a $sim10^{-3}$ M$_{odot}$ companion in a 7.75-hour circular orbit. Follow-up observations at the Parkes and Lovell telescopes have led to precise measurements of the astrometric and spin parameters, including the period derivative, timing parallax, and proper motion. PSR J2322$-$2650 has a parallax of $4.4pm1.2$ mas, and is thus at an inferred distance of $230^{+90}_{-50}$ pc, making this system a candidate for optical studies. We have detected a source of $Rapprox26.4$ mag at the radio position in a single $R$-band observation with the Keck Telescope, and this is consistent with the blackbody temperature we would expect from the companion if it fills its Roche lobe. The intrinsic period derivative of PSR J2322$-$2650 is among the lowest known, $4.4(4)times10^{-22}$ s s$^{-1}$, implying a low surface magnetic field strength, $4.0(4)times10^7$ G. Its mean radio flux density of 160 $mu$Jy combined with the distance implies that its radio luminosity is the lowest ever measured, $0.008(5)$ mJy kpc$^2$. The inferred population of these systems in the Galaxy may be very significant, suggesting that this is a common MSP evolutionary path.
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