A place cell is a neuron that fires whenever the animal traverses a particular location of the environment-the place field of the cell. Place cells are found in two regions of the rodent hippocampus: CA3 and CA1. Motivated by the anatomical connectivity between these two regions and by the evidence for synaptic plasticity at these connections, we study how a place field in CA1 can be inherited from an upstream region such as CA3 through a Hebbian learning rule, in particular, through spike-timing-dependent plasticity (STDP). To this end, we model a population of CA3 place cells projecting to a single CA1 cell, and we assume that the CA1 input synapses are plastic according to STDP. With both numerical and analytical methods, we show that in the case of overlapping CA3 input place fields, the STDP learning rule leads to the formation of a place field in CA1. We then investigate the roles of the hippocampal theta modulation and phase precession on the inheritance process. We find that theta modulation favors the inheritance and leads to faster place field formation whereas phase precession changes the drift of CA1 place fields over time.