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K2-139 b is a warm Jupiter with an orbital period of 28.4 d, but only three transits of this system have previously been observed, in the long-cadence mode of K2, limiting the precision with which the orbital period can be determined, and future transits predicted. We report photometric observations of four transits of K2-139 b with ESA's CHaracterising ExOPlanet Satellite (CHEOPS), conducted with the goal of measuring the orbital obliquity via spot-crossing events. We jointly fit these CHEOPS data alongside the three previously-published transits from the K2 mission, considerably increasing the precision of the ephemeris of K2-139 b. The transit times for this system can now be predicted for the next decade with a $1 σ$ precision less than 10 minutes, compared to over one hour previously, allowing the efficient scheduling of observations with Ariel. We detect no significant deviation from a linear ephemeris, allowing us to exclude the presence of a massive outer planet orbiting with a period less than 150 d, or a brown dwarf with a period less than one year. We also determine the scaled semi-major axis, the impact parameter, and the stellar limb-darkening with improved precision. This is driven by the shorter cadence of the CHEOPS observations compared to that of K2, and validates the sub-exposure technique used for analysing long-cadence photometry. Finally, we note that the stellar spot configuration has changed from the epoch of the K2 observations; unlike the K2 transits, we detect no evidence of spot-crossing events in the CHEOPS data.