Long Range (LoRa) is an emerging low-power wide-area network technology offering long-range wireless connectivity to Internet of Things (IoT) devices. For energy efficiency reasons, LoRa end nodes implement a nonslotted ALOHA multiple access scheme to transmit packets to the gateway. Due to the lack of synchronization between end nodes, collisions between uplink packets have been identified as the main obstacle to the scaling of dense LoRa networks. To tackle this issue, we present in this article a LoRa receiver that is capable of decoding colliding packets from two interfering end nodes. The proposed two-user detector is derived from the maximum-likelihood principle using a detailed model of two colliding LoRa packets. As the complexity of the maximum-likelihood sequence estimation is prohibitive, complexity-reduction techniques are introduced to enable practical implementations of the receiver. An in-depth performance analysis highlights that the proposed two-user detector inherently leverages the differences in received power, time offsets, and frequency offsets between the users to separate and demodulate their respective signals. To demonstrate the practicality of the proposed detector, an interference-robust synchronization algorithm is then designed and evaluated. Simulation results indicate that a LoRa receiver combining the proposed synchronization algorithm and two-user detector is capable of detecting and demodulating two interfering users with satisfactorily error rates.