This thesis describes the search for and eventual detection of very high energy gamma-ray emission from the galactic binary LS I +61 303 utilizing both the Fred Lawrence Whipple 10 meter atmospheric Cherenkov telescope as well as VERITAS, which is a newly constructed array of atmospheric Cherenkov telescopes; both sensitive in the TeV gamma-ray regime. Although the source was not detected with the Whipple 10 m telescope, flux upper limits were placed on its emission above >540 GeV. Observations of LS I +61 303 were conducted with the VERITAS array in the 2006/2007 observing season resulting in a detection of the source in> 310 GeV gamma-rays at a 7.23cr significance. Along with the detection in very high energy gamma-rays by VERITAS, contemporaneous observations of LS I +61 303 in the hard X-ray regime with the Rossi X-ray Timing Explorer and Swift satellites are described. All three sets of observations show LS 1+61 303 to be a variable source in both energy regimes, with this variability associated with changes in the 26.496 day orbital cycle of the binary system. A search for correlation between emission in both the hard X-ray and energy regimes is carried out with no statistically viable correlation found. The two most basic models built to describe the system (i.e. rnicroquasar _ __ __ __ _ ~~bina!Y pulsar) are described in detail and compared to the available observations. --- -- --'- -------'------_._----- - ._~ It is found __. --------_ -.:'.-:-- _ _'.-_._._---------._------_._------------ that neither model satisfactorily describes the emission properties of the system as detailed in this work.