IGR J17091–3624 is a black hole X-ray binary (BHXB), often referred to as the "twin" of GRS 1915+105 because it is the only other known BHXB that can show exotic "heartbeat"-like variability that is highly structured and repeated. Here, we report on observations of IGR J17091–3624 from its 2022 outburst, where we detect an unusually coherent quasiperiodic oscillation (QPO) when the broadband variability is low (total fractional rms ≲6%) and the spectrum is dominated by the accretion disk. Such spectral and variability behavior is characteristic of the soft state of typical BHXBs (i.e., those that do not show heartbeats), but we also find that this QPO is strongest when there is some exotic heartbeat-like variability (so-called Class V variability). This QPO is detected at frequencies between 5 and 8 Hz and has Q factors (defined as the QPO frequency divided by the width) ≳50, making it one of the most highly coherent low-frequency QPOs ever seen in a BHXB. The extremely high Q factor makes this QPO distinct from typical low-frequency QPOs that are conventionally classified into type-A/B/C QPOs. Instead, we find evidence that archival observations of GRS 1915+105 also showed a similarly high-coherence QPO in the same frequency range, suggesting that this unusually coherent and strong QPO may be unique to BHXBs that can exhibit "heartbeat"-like variability.