The power target for exascale supercomputing is 20MW, with about 30% budgeted for the memory subsystem. Commodity DRAMs will not satisfy this requirement. Additionally, the large number of memory chips (>10M) required will result in crippling failure rates. Although specialized DRAM memories have been reorganized to reduce power through 3D-stacking or row buffer resizing, their implications on fault tolerance have not been considered. We show that addressing reliability and energy is a co-optimization problem involving tradeoffs between error correction cost, access energy and refresh power---reducing the physical page size to decrease access energy increases the energy/area overhead of error resilience. Additionally, power can be reduced by optimizing bitline lengths. The proposed 3D-stacked memory uses a page size of 4kb and consumes 5.1pJ/bit based on simulations with NEK5000 benchmarks. Scaling to 100PB, the memory consumes 4.7MW at 100PB/s which, while well within the total power budget (20MW), is also error-resilient.