Meeting desired application deadlines in cloud processing systems such as MapReduce is crucial as the nature of cloud applications is becoming increasingly mission-critical and deadline-sensitive. It has been shown that the execution times of MapReduce jobs are often adversely impacted by a few slow tasks, known as stragglers, which result in high latency and deadline violations. While a number of strategies have been developed in existing work to mitigate stragglers by launching speculative or clone task attempts, none of them provides a quantitative framework that optimizes the speculative execution for offering guaranteed Service Level Agreements (SLAs) to meet application deadlines. In this paper, we bring several speculative scheduling strategies together under a unifying optimization framework, called Chronos, which defines a new metric, Probability of Completion before Deadlines (PoCD), to measure the probability that MapReduce jobs meet their desired deadlines. We systematically analyze PoCD for popular strategies including Clone, Speculative-Restart, and Speculative-Resume, and quantify their PoCD in closed-form. The result illuminates an important tradeoff between PoCD and the cost of speculative execution, measured by the total (virtual) machine time required under different strategies. We propose an optimization problem to jointly optimize PoCD and execution cost in different strategies, and develop an algorithmic solution that is guaranteed to be optimal. Chronos is prototyped on Hadoop MapReduce and evaluated against three baseline strategies using both experiments and trace-driven simulations, achieving 50% net utility increase with up to 80% PoCD and 88% cost improvements.