The longitudinal double-spin asymmetry

(A\textsubscript{LL}) in spin-polarized \emph{p+p} collisions provides insight into the gluon contribution to the proton's spin by accessing the gluon helicity distribution $\Delta$g. Prior PHENIX $\pi$\textsuperscript{0} and STAR jet A\textsubscript{LL} measurements show a non-zero asymmetries and hence indicate a nonzero $\Delta$g in an NLO analysis. The STAR measurements of jet A\_LL in $\surd$s = 200 and 510 GeV polarized p+p collisions provide the strongest constraints on $\Delta$g at intermediate to high \textit{x}. A measurement of the jet A\textsubscript{LL} at $\surd$s = 510 GeV in PHENIX will provide an important cross-check. This thesis will detail the jet reconstruction techniques tuned for the PHENIX detector and present the

measured jet A\textsubscript{LL}.