Context. The star HD 139139 (a.k.a. ‘the Random Transiter’) is a star that exhibited enigmatic transit-like features with no apparent periodicity in K2 data. The shallow depth of the events (~200 ppm – equivalent to transiting objects with radii of ~1.5 R_⊕ in front of a Sun-like star) and their non-periodicity constitute a challenge for the photometric follow-up of this star. Aims. The goal of this study is to confirm with independent measurements the presence of shallow, non-periodic transit-like features on this object. Methods. We performed observations with CHEOPS for a total accumulated time of 12.75 days, distributed in visits of roughly 20 h in two observing campaigns in years 2021 and 2022. The precision of the data is sufficient to detect 150 ppm features with durations longer than 1.5 h. We used the duration and times of the events seen in the K2 curve to estimate how many events should have been detected in our campaigns, under the assumption that their behaviour during the CHEOPS observations would be the same as in the K2 data of 2017. Results. We do not detect events with depths larger than 150 ppm in our data set. If the frequency, depth, and duration of the events were the same as in the K2 campaign, we estimate the probability of having missed all events due to our limited observing window would be 4.8%. Conclusions. We suggest three different scenarios to explain our results: 1) Our observing window was not long enough, and the events were missed with the estimated 4.8% probability. 2) The events recorded in the K2 observations were time critical, and the mechanism producing them was either not active in the 2021 and 2022 campaigns or created shallower events under our detectability level. 3) The enigmatic events in the K2 data are the result of an unidentified and infrequent instrumental noise in the original data set or its data treatment.