We study the frictional drag between carriers in two bilayer graphene flakes separated by a 2-5 nm thick hexagonal boron nitride dielectric. At temperatures (T) lower than ∼10 K, we observe a large anomalous negative drag emerging predominantly near the drag layer charge neutrality. The anomalous drag resistivity increases dramatically with reducing T, and becomes comparable to the layer resistivity at the lowest T=1.5 K. At low T the drag resistivity exhibits a breakdown of layer reciprocity. A comparison of the drag resistivity and the drag layer Peltier coefficient suggests a thermoelectric origin of this anomalous drag.