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The present paper extends the classically studied chance-constrained optimal control to incorporate continuous-time chance constraints. While the classical approaches provide risk guarantees only at discretized epochs, it is essential for most physical systems to have continuous-time risk guarantees; it is especially important for unstable systems. This paper develops a new approach to enforce continuous-time risk guarantees by leveraging a notion of Cumulative Lyapunov Exponent, which measures the cumulative stabilities of Linear Time-Varying (LTV) systems. The solution method finds a sequence of feedback control policies for LTV systems that minimizes the expected control cost subject to continuous-time chance constraints. We demonstrate the approach with a spacecraft orbit control scenario on an unstable orbit. Monte Carlo simulations with the optimized feedback policies show that our approach respects the continuous-time chance constraints whereas a classical approach results in the constraint violation between the discretized epochs.