The computational and memory challenges of large language models (LLMs) have sparked several optimization approaches towards their efficient implementation. While prior LLM-targeted quantization, and prior works on sparse acceleration have significantly mitigated the memory and computation bottleneck, they do so assuming high power platforms such as GPUs and server-class FPGAs with large off-chip memory bandwidths and employ a generalized matrix multiplication (GEMM) execution of all the layers in the decoder. In such a GEMM-based execution, data is fetched from an off-chip memory, computed and stored back. However, at reduced off-chip memory capacities, as is the case with low-power edge devices, this implementation strategy significantly increases the attention computation latency owing to the repeated storage and fetch of large intermediate tokens to and from the off-chip memory. Moreover, fetching the weight matrices from a bandwidth constrained memory further aggravates the memory bottleneck problem. To this end, we introduce MEADOW, a framework that significantly reduces the off-chip memory access for LLMs with a novel token-parallel head-sequential (TPHS) dataflow. Additionally, MEADOW applies weight packing that performs loss-less decomposition of large weight matrices to their unique elements thereby, reducing the enormous weight fetch latency. MEADOW demonstrates 1.5x and 2.5x lower decode and prefill latency, respectively, compared to a GEMM-based LLM implementation on the low power Xilinx ZCU102 FPGA platform that consumes less than 10W. Additionally, MEADOW achieves an end-to-end latency improvement of over 40%, compared to prior LLM optimization works.