We have discovered strong gravitational lensing features in the core of the nearby cluster Abell 3827 by analyzing Gemini South GMOS images. The most prominent strong lensing feature is a highly-magnified, ring-shaped configuration of four images around the central cD galaxy. GMOS spectroscopic analysis puts this source at z~0.2. Located ~20 away from the central galaxy is a secondary tangential arc feature which has been identified as a background galaxy with z~0.4. We have modeled the gravitational potential of the cluster core, taking into account the mass from the cluster, the BCG and other galaxies. We derive a total mass of (2.7 +- 0.4) x 10^13 Msun within 37 h^-1 kpc. This mass is an order of magnitude larger than that derived from X-ray observations. The total mass derived from lensing data suggests that the BCG in this cluster is perhaps the most massive galaxy in the nearby Universe.