An emergent literature has shown that some students overcome adversities related to their low Socio-Economic Status (SES) by attaining high academic achievement. One of the aims of this literature is to identify the factors that explain the capacity of students from low SES backgrounds to attain high academic achievement. However, upon reviewing this literature, I observed that few studies have comparatively investigated the associations between the capacity of students from low SES backgrounds to attain high achievement in reading and school climate characteristics. Additionally, I found that not many studies have researched whether student SES moderates these associations. This paper contributes to fill these two gaps by estimating associations between high achievement in reading and school climate characteristics. Moreover, it examines whether student SES moderates these associations. To do this, this research estimated logit and heterogeneous choice models using representative samples of students from Argentina, Brazil, Chile, Colombia, and Uruguay who participated in the 2018 Programme for International Student Assessment (PISA). The results show that high achievement in reading is positively correlated to certain teaching practices, such as perceived teacher enthusiasm during the instruction and adapting instruction to students' needs. Conversely, it is negatively correlated to teacher feedback and teacher-directed instruction. Furthermore, the findings indicate that high achievement in reading is negatively correlated to the scarcity and low quality of educational material. Interestingly, the results show that student SES does not moderate these associations. In conclusion, these findings indicate that interventions targeting these areas of school climate may help to increase students' probability of attaining high achievement in reading, regardless of their SES. Likewise, these results suggest that if these interventions are focused in low SES schools, they may contribute to bridge the gap in reading skills between students from low and middle or high socioeconomic backgrounds.