We report on deep imaging of a remote M31 globular cluster, MGC1, obtained with Gemini/GMOS. Our colour-magnitude diagram for this object extends similar to 5 mag below the tip of the red-giant branch and exhibits features consistent with an ancient metal-poor stellar population, including a long, well-populated horizontal branch. The red-giant branch locus suggests MGC1 has a metal abundance [M/H] approximate to -2.3. We measure the distance to MGC1 and find that it lies similar to 160 kpc in front of M31 with a distance modulus mu = 23.95 +/- 0.06. Combined with its large projected separation of R-p = 117 kpc from M31, this implies a deprojected radius of R-gc = 200 +/- 20 kpc, rendering it the most isolated known globular cluster in the Local Group by some considerable margin. We construct a radial brightness profile for MGC1 and show that it is both centrally compact and rather luminous, with M-V = -9.2. Remarkably, the cluster profile shows no evidence for a tidal limit and we are able to trace it to a radius of at least 450 pc, and possibly as far as similar to 900 pc. The profile exhibits a power-law fall-off with exponent gamma = -2.5, breaking to gamma = -3.5 in its outermost parts. This core-halo structure is broadly consistent with expectations derived from numerical models, and suggests that MGC1 has spent many gigayears in isolation.