Semiconductor nanowires coupled to a superconductor provide a powerful testbed for quantum device physics such as Majorana zero modes and gate-tunable hybrid qubits. The performance of these quantum devices heavily relies on the quality of the induced superconducting gap. A hard gap, evident as vanishing subgap conductance in tunneling spectroscopy, is both necessary and desired. Previously, a hard gap has been achieved and extensively studied in III-V semiconductor nanowires (InAs and InSb). In this study, we present the observation of a hard superconducting gap in PbTe nanowires coupled to a superconductor Pb. The gap size ($\Delta$) is $\sim$ 1 meV (maximally 1.3 meV in one device). Additionally, subgap Andreev bound states can also be created and controlled through gate tuning. Tuning a device into the open regime can reveal Andreev enhancement of the subgap conductance, suggesting a remarkable transparent superconductor-semiconductor interface, with a transparency of $\sim$ 0.96. These results pave the way for diverse superconducting quantum devices based on PbTe nanowires.