Low Earth Orbit (LEO) satellite networks provide global data service coverage and has become increasingly popular. Uncoordinated access channels reduce data latency in LEO networks by allowing user terminals to transmit data packets at random times to the satellite without any coordination overhead. In this paper, packet acquisition in uncoordinated access channels of LEO networks is studied and a novel solution, called ChirpPair, is proposed, with which the satellite can detect the packets as well as estimating key parameters of the packets for data demodulation. With ChirpPair, the packet preamble consists of a chirp and its conjugate, where a chirp is a complex vector with constant magnitude and linearly increasing frequency. ChirpPair adopts a multi-stage process that gradually increases the estimation accuracy of the parameters without incurring high computation complexity. ChirpPair has been demonstrated in real-world experiments with over-the-air transmissions. ChirpPair has also been evaluated by simulations with the 3GPP New Radio (NR) Non-Terrestrial Network (NTN) channel model and the results show that ChirpPair achieves high accuracy despite its low computation complexity.