To efficiently and effectively debug silicon bugs, a promising solution is to determinize the chip, so that the buggy silicon behaviors can be faithfully reproduced on a RTL simulator. In this paper, we propose a novel scheme, named LDet, to determinize a chip through removing the nondeterminism in transfers crossing different clock domains, even when these clock domains are heterochronous. The key insight of LDet is that we can slightly adjust the frequencies of clocks at runtime so that the actual frequency ratio between two clocks always approaches a rational constant with bounded accumulated error. With the technique called dynamic frequency adjusting, the processing time of each asynchronous transfer can be determinized with deterministic asynchronous fifo (DAF). As a consequence, the behavior of the whole chip is deterministic, thus the chip behavior can be reproduced on the RTL simulator (given the same initial state and input sequence). We implement LDet on the RTL design of a processor chip with many clock domains. Experiments show that on average, LDet only causes about one cycle of additional latency to each asynchronous transfer. As a result, LDet only incurs a negligible performance overhead of about 0.7 percent slowdown. Moreover, LDet only brings less than 0.2 percent additional area to the chip. The low performance and area overheads of LDet well demonstrate its applicability in industry.