Aims. The aim of this study is to investigate the structure and kinematics of the nearby candidate first hydrostatic core Cha-MMS1. Methods. Cha-MMS1 was mapped in the NH3(1, 1) line and the 1.2 cm continuum using the Australia Telescope Compact Array (ATCA). The angular resolution of the ATCA observations is 7 '' (similar to 1000 AU), and the velocity resolution is 50 m s(-1). The core was also mapped with the 64 m Parkes Telescope in the NH3(1, 1) and (2, 2) lines. Observations from Herschel Space Observatory and Spitzer Space Telescope were used to help interpretation. The ammonia spectra were analysed using Gaussian fits to the hyperfine structure. A two-layer model was applied in the central parts of the core where the ATCA spectra show signs of self-absorption. Results. A compact high column density core with a steep velocity gradient (similar to 20 km s(-1) pc(-1)) is detected in ammonia. We derive a high gas density (similar to 10(6) cm(-3)) in this region, and a fractional ammonia abundance compatible with determinations towards other dense cores (similar to 10(-8)). This suggests that the age of the high density core is comparable to the freeze-out timescale of ammonia in these conditions, on the order of 10(4) years. The direction of the velocity gradient agrees with previous single-dish observations, and the overall velocity distribution can be interpreted as rotation. The rotation axis goes through the position of a compact far-infrared source detected by Spitzer and Herschel. The specific angular momentum of the core, similar to 10(-3) km s(-1) pc, is typical for protostellar envelopes. A string of 1.2 cm continuum sources is tentatively detected near the rotation axis. The ammonia spectra suggest the presence of warm embedded gas in its vicinity. An hourglass-shaped structure is seen in ammonia at the cloud's average LSR velocity, also aligned with the rotation axis. Although this structure resembles a pair of outflow lobes the ammonia spectra show no indications of shocked gas. Conclusions. The observed ammonia structure mainly delineates the inner envelope around the central source. The velocity gradient is likely to originate in the angular momentum of the contracting core, although influence of the outflow from the neighbouring young star IRS4 is possibly visible on one side of the core. The tentative continuum detection and the indications of a warm background component near the rotation axis suggest that the core contains a deeply embedded outflow which may have been missed in previous single-dish CO surveys owing to beam dilution.