Fast carry chains featuring dedicated adder circuitry is a distinctive feature of modern FPGAs. The carry chains bypass the general routing network and are embedded in the logic blocks of FPGAs for fast addition. Conventional intuition is that such carry chains can be used only for implementing carry-propagate addition; state-of-the-art FPGA synthesizers can only exploit the carry chains for these specific circuits. This paper demonstrates that the carry chains can be used to build compressor trees, i.e., multi-input addition circuits used for parallel accumulation and partial product reduction for parallel multipliers implemented in FPGA logic. The key to our technique is to program the lookup tables (LUTs) in the logic blocks to stop the propagation of carry bits along the carry chain at appropriate points. This approach improves the area of compressor trees significantly compared to previous methods that synthesized compressor trees solely on LUTs, without compromising the performance gain over trees built from ternary carry-propagate adders.