Context. While many hot Jupiter systems have an obliquity measurement, the data on warm Jupiter systems are lacking. The longer orbital periods and transit durations of warm Jupiters make it more difficult to measure the obliquities of their host stars. However, the longer periods also mean that any misalignments persist due to the longer tidal realignment timescales. As a result, measuring these obliquities is necessary to improve our understanding how these types of planets form and how their formation and evolution differ from the processes characterizing hot Jupiters. Aims. Here, we report the measurement of the Rossiter-McLaughlin effect for the TOI-4127 system using the HARPS-N spectrograph. Methods. We modeled the system using our new HARPS-N radial velocity measurements, along with archival TESS photometry and NEID and SOPHIE radial velocities. Results. We find that the host star is well-aligned with the highly eccentric (e=0.75) warm Jupiter TOI-4127 b, with a sky-projected obliquity of λ = 4−16+17∘. This makes TOI-4127 one of the most eccentric well-aligned systems to date and one of the longest periods for a system with a measured obliquity. Conclusions. The origin of its highly eccentric, yet well-aligned orbit remains a mystery, however, and we investigate possible scenarios that could explain it. While typical in situ formation and disk migration scenarios cannot explain this system, certain scenarios involving resonant interactions between the planet and protoplanetary disk could. Similarly, specific cases of planet-planet scattering or Kozai-Lidov oscillations can result in a highly-eccentric and well-aligned orbit. Coplanar high-eccentricity migration could also explain this system. However, scenarios involvng this mechanism or Kozai-Lidov oscillations would require an additional planet in the system, which has not yet been detected in this case.