The presence of lithium rich giant stars has been a long unresolved question in astrophysics. Lithium is extremely vulnerable to the mixing processes in giant stars where it can be easily destroyed. However, roughly one percent of giant stars have been shown to have some level of lithium enhancement, with around 150 being discovered in the last 3 decades. Of these, only four have been reported to have an ALi > 4.0. We present a detailed abundance analysis of 2MASS J05241392-0336543, a metal-poor Milky Way halo star ([Fe/H]=-2.3) with an ALi(LTE) = 6.24, thus making it the most lithium enhanced giant discovered to date. Analysis of its stellar parameters on the HR diagram indicates that this star is an asymptotic giant branch star. Most other Li enhanced giants have been shown to be RGB stars. We further investigate the source of lithium enhancement in our star. Possible candidates include planetary engulfment, non-standard mixing models, an after-effect of the helium flash, as well as other factors. The cosmological abundance of lithium is still an open question given the theoretical value is greater than the observed value by a factor of ~3. The lithium enhancement in our star is far larger than that of both the observed and predicted primordial lithium abundance for a metal-poor star. This indicated towards a non-trivial mechanism to produce or accrete lithium. The discovery of such a mechanism could have profound effects on our understanding of open questions regarding the cosmological lithium problem.