  We report the detection of orbital modulation, a model solution, and X-ray
properties of a newly discovered contact binary, 2MASS J11201034$-$2201340. We
serendipitously found this X-ray point source outside the error ellipse when
searching for possible X-ray counterparts of $\gamma$-ray millisecond pulsars
among the unidentified objects detected by the {\it Fermi Gamma-ray Space
Telescope}. The optical counterpart of the X-ray source (unrelated to the
$\gamma$-ray source) was then identified using archival databases. The
long-term CRTS survey detected a precise signal with a period of
$P=0.28876208(56)$ days. A follow-up observation made by the SLT telescope of
Lulin Observatory revealed the binary nature of the object. Utilizing archived
photometric data of multi-band surveys, we construct the spectral energy
distribution, which is well fitted by a K2V spectral template. The fitting
result of the orbital profile using the Wilson--Devinney code suggests that
2MASS J11201034-2201340 is a short-period A-type contact binary and the more
massive component has a cool spot. The X-ray emission was first noted in
observations made by \swift\, then further confirmed and characterized by an
\xmm\ observation. The X-ray spectrum can be described by a power law or
thermal Bremsstrahlung. Unfortunately, we could not observe significant X-ray
orbital modulation. Finally, according to the spectral energy distribution,
this system is estimated to be 690 pc from Earth with a calculated X-ray
intensity of $(0.7-1.5)\times 10^{30}$ erg s$^{-1}$, which is in the expected
range of an X-ray emitting contact binary.
