We present a detailed study of a bipolar, possible Type I planetary nebula (PN), PHR 1315−6555 (PN G305.3−03.1), which was discovered as part of the Macquarie/AAO/Strasbourg Hα planetary nebula project (MASH), and that we considered at the time was an excellent candidate for membership of the distant, compact, intermediate-age open cluster, ESO 96-SC04. The strong evidence for this association is presented here, making this the only known example of a PN physically associated with a Galactic open cluster. Cluster membership is extremely important as it allows for very precise estimates of the fundamental properties of the PN as the cluster is at a known distance. The PN was discovered by one of us (QAP) during systematic MASH searches for new Galactic PNe of the AAO United Kingdom Schmidt Telescope (UKST) Hα survey and had been missed in earlier broad-band surveys, including specific CCD studies of the host cluster. We present original discovery images and Cerro Tololo Inter-American Observatory (CTIO) 4-m MOSAIC-II camera follow-up narrow-band images that reveal its bipolar morphology. We also present (i) low-resolution optical spectra that spectroscopically confirm the PN, (ii) accurate radial velocities of PN and cluster stars from high-resolution spectroscopy which show they are consistent and (iii) a reliable, independent distance estimate to the PN using a robust PN distance indicator which agrees with the published cluster distance to within the errors. We also provide preliminary estimates of basic PN properties and abundance estimates from deeper spectra that show it to be of possible Type I chemistry. This is also consistent with its estimated turn-off mass. Taken together, these findings present a powerful case for clear physical association between the PN and host cluster. Results for this association will be of considerable interest to specialists across differing astrophysical disciplines, including PNe, white dwarfs and open clusters.