With the rapidly growing use of Convolutional Neural Networks (CNNs) in real-world applications related to machine learning and Artificial Intelligence (AI), several hardware accelerator designs for CNN inference and training have been proposed recently. In this paper, we present ATRIA, a novel bit-pArallel sTochastic aRithmetic based In-DRAM Accelerator for energy-efficient and high-speed inference of CNNs. ATRIA employs light-weight modifications in DRAM cell arrays to implement bit-parallel stochastic arithmetic based acceleration of multiply-accumulate (MAC) operations inside DRAM. ATRIA significantly improves the latency, throughput, and efficiency of processing CNN inferences by performing 16 MAC operations in only five consecutive memory operation cycles. We mapped the inference tasks of four benchmark CNNs on ATRIA to compare its performance with five state-of-the-art in-DRAM CNN accelerators from prior work. The results of our analysis show that ATRIA exhibits only 3.5% drop in CNN inference accuracy and still achieves improvements of up to 3.2x in frames-per-second (FPS) and up to 10x in efficiency (FPS/W/mm2), compared to the best-performing in-DRAM accelerator from prior work.