  We analyze the microlensing event KMT-2019-BLG-0797. The light curve of the
event exhibits two anomalous features from a single-lens single-source model,
and we aim to reveal the nature of the anomaly. It is found that a model with
two lenses plus a single source (2L1S model) can explain one feature of the
anomaly, but the other feature cannot be explained. We test various models and
find that both anomalous features can be explained by introducing an extra
source to a 2L1S model (2L2S model), making the event the third confirmed case
of a 2L2S event, following on MOA-2010-BLG-117 and OGLE-2016-BLG-1003. It is
estimated that the extra source comprises $\sim 4\%$ of the $I$-band flux from
the primary source. Interpreting the event is subject to a close--wide
degeneracy. According to the close solution, the lens is a binary consisting of
two brown dwarfs with masses $(M_1, M_2)\sim (0.034, 0.021)~M_\odot$, and it is
located at a distance of $\dl\sim 8.2$~kpc. According to the wide solution, on
the other hand, the lens is composed of an object at the star/brown-dwarf
boundary and an M dwarf with masses $(M_1, M_2)\sim (0.06, 0.33)~M_\odot$
located at $\dl\sim 7.7$~kpc. The source is composed of a
late-G-dwarf/early-K-dwarf primary and an early-to-mid M-dwarf companion.
