The healing of broken chromosomes by de novo telomere addition, while a normal developmental process in some organisms, has the potential to cause extensive loss of heterozygosity, genetic disease, or cell death. However, it is unclear how de novo telomere addition (dnTA) is regulated at DNA double-strand breaks (DSBs). Here, using a non-essential minichromosome in fission yeast, we identify roles for the HR factors Rqh1 helicase, in concert with Rad55, in suppressing dnTA at or near a DSB. We find the frequency of dnTA in rqh1Δ rad55Δ cells is reduced following loss of Exo1, Swi5 or Rad51. Strikingly, in the absence of the distal homologous chromosome arm dnTA is further increased, with nearly half of the breaks being healed in rqh1Δ rad55Δ or rqh1Δ exo1Δ cells. These findings provide new insights into the genetic context of highly efficient dnTA within HR intermediates, and how such events are normally suppressed to maintain genome stability.