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The earliest stages of low-mass star-formation are unclear, but it has been proposed that Chamaeleon-MMS1 is a candidate First Hydrostatic Core (FHSC), the transition stage between a prestellar and protostellar core. This work describes the local (~4000 AU) outflow activity associated with Chamaeleon-MMS1 and its effect on the surrounding material in order to determine the evolutionary state of this young low-mass source. We used the Atacama Large Millimeter/sub-millimeter Array (ALMA) to observe Chamaeleon MMS1 at 220 GHz at high spatial (~75 AU) and spectral resolutions (0.1-0.3 km/s). A low energy outflow is detected through its interaction with the surrounding cloud. The outflow consists of two components, a broad spectral feature to the northeast and narrow features to both the northeast and southwest. The rotational temperature of formaldehyde (H2CO) is calculated to be 50 (+/-30) K toward the continuum source with similarly low temperatures (25-45 K) toward clumps affected by the outflow. Methanol (CH3OH) is only detected toward gas clumps located away from the continuum source, where the methanol is expected to have been released by the energy of the outflow through ice sputtering in shock waves. Chamaeleon-MMS1 shows outflow activity with the power source being either a single precessing outflow or two outflows from a binary system. While molecular emission and high outflow speeds rule it out as a FHSC, the outflow is less energetic than outflows detected from other Class 0 objects and the inferred gas temperatures toward the continuum source are relatively low, which indicates that Cha-MMS1 is one of the youngest known sources.