Telomere integrity is maintained through end-protection proteins that block nuclease degradation and prevent telomeres from being recognized as DNA breaks. Although less well understood, end protection proteins may also play a role in facilitating telomere replication. Here, we show that overproduction (OP) of the yeast telomere capping protein Stn1 makes cells highly sensitive to the replication inhibitors hydroxyurea (HU) and methyl-methane sulfonate (MMS). Unexpectedly, this sensitivity corresponds with Stn1 OP blocking most, if not all, aspects of the S phase checkpoint. The checkpoint kinase Rad53 is phosphorylated with normal timing in Stn1 OP cells, indicating Stn1 does not interfere with signaling steps involved in activating the checkpoint. Part of the role of Stn1 in telomere integrity is mediated through the Pol12 subunit of DNA polymerase α (Polα). We show that overproduced Stn1 generally associates with chromosomes in HU treated and untreated cells, and, remarkably, Stn1 chromosome binding and OP checkpoint defects are rescued in pol12 mutants. We propose Stn1 normally promotes Polα activity at telomeres but can be recruited through Pol12 to nontelomeric sites when overproduced. During replication stress, the mislocalized Stn1 may inappropriately promote Polα in a manner that interferes with Rad53 effector mechanisms controlling replication fork integrity.