Stochastic optimal control based powered descent guidance (SOC-PDG) transforms the powered descent guidance problem with uncertainties into a stochastic optimal control framework, representing a key technology for enhancing the reliability of reusable rockets. However, under a wide range of initial state and uncertainty distribution combinations, existing SOC-PDG methods based on mean-covariance constraint descriptions are unable to handle potentially long-tailed terminal state distributions, making it difficult to effectively manage low-probability but catastrophic large-magnitude terminal errors. To address this, this paper investigates the SOC-PDG problem with landing chance constraints (SOC-PDG-LCC), which directly introduce landing chance constraints related to the quantiles of the terminal state distribution. To tackle the high sensitivity, low evaluation efficiency, and non-differentiability of the landing chance constraints, this paper designs a guidance policy with the following key features: 1) An improved neural network-based parametric guidance architecture is employed to maintain consistent landing performance across different initial state and uncertainty distribution parameters. 2) A guidance policy evaluation method based on the polynomial chaos expansion surrogate model is proposed to enable efficient estimation of the mean propellant consumption and the quantiles for landing chance constraints during training. 3) A reinforcement learning training method for the guidance policy is developed using samples from the surrogate model, achieving gradient-free optimization of the guidance policy. Simulation results demonstrate that, compared to existing SOC-PDG methods based on mean-covariance constraint descriptions, the proposed method effectively mitigates the long-tail characteristics of the terminal state distribution across a wide range of initial states and uncertainty parameters, significantly reducing the probability of low-probability landing failure events.