Inspired by several delay-bounded mission-critical applications, this paper investigates chase-combining-based hybrid automatic repeat request (CC-HARQ) protocols to achieve high reliability in delay-constrained applications. A salient feature of our approach is to use the end-to-end delay constraint for computing the total number of ARQs permitted in the network, and then optimally distributing them across the nodes so as to minimize packet-drop-probability (PDP), which is the end-to-end reliability metric of interest. Since the chase-combining strategy combines the received packets across multiple attempts, we observe that the PDP of the network depends on the coherence-time of the intermediate wireless channels. As a result, we address the question of computing optimal allocation of ARQs for CC-HARQ strategies under both slow-fading and fast-fading scenarios. For both the channel conditions, we derive closed-form expressions for the PDP, and then formulate several optimization problems for minimizing the PDP for a given delay-bound. Using extensive theoretical results on the local minima of the optimization problems, we synthesize low-complexity algorithms to obtain near-optimal ARQ distributions. Besides using extensive simulation results to validate our findings, a detailed end-to-end delay analysis is also presented to show that the proposed CC-HARQ strategies outperform already known Type-1 ARQ based strategies in several scenarios.