Context: The mechanism of radio emission in radio-quiet (RQ) active galactic nuclei (AGNs) is still debated and might arise from the central AGN, from star formation activity in the host, or from either of these sources. A direct detection of compact and bright radio cores embedded in sources that are classified as RQ can unambiguously determine whether a central AGN significantly contributes to the radio emission. Aims: We search for compact, high-surface-brightness radio cores in RQ AGNs that are caused unambiguously by AGN activity. Methods: We used the Australian Long Baseline Array to search for compact radio cores in four RQ AGNs located in the Extended Chandra Deep Field South (ECDFS). We also targeted four radio-loud (RL) AGNs as a control sample. Results: We detected compact and bright radio cores in two AGNs that are classified as RQ and in one that is classified as RL. Two RL AGNs were not imaged because the quality of the observations was too poor. Conclusions: We report on a first direct evidence of radio cores in RQ AGNs at cosmological redshifts. Our detections show that some of the sources that are classified as RQ contain an active AGN that can contribute significantly (~50% or more) to the total radio emission. ; 4 page(s)