Given a set of $n$ points in $\ell_1$, how many dimensions are needed to represent all pairwise distances within a specific distortion? This dimension-distortion tradeoff question is well understood for the $\ell_2$ norm, where $O((\log n)/\epsilon^{2})$ dimensions suffice to achieve $1+\epsilon$ distortion. In sharp contrast, there is a significant gap between upper and lower bounds for dimension reduction in $\ell_1$. A recent result shows that distortion $1+\epsilon$ can be achieved with $n/\epsilon^{2}$ dimensions. On the other hand, the only lower bounds known are that distortion $\delta$ requires $n^{\Omega(1/\delta^2)}$ dimensions and that distortion $1+\epsilon$ requires $n^{1/2-O(\epsilon \log(1/\epsilon))}$ dimensions. In this work, we show the first near linear lower bounds for dimension reduction in $\ell_1$. In particular, we show that $1+\epsilon$ distortion requires at least $n^{1-O(1/\log(1/\epsilon))}$ dimensions. Joint work with Moses Charikar, Ofer Neiman, and Huy L. Nguyen.