In view of the considerable and growing number of non-native EFL/ESL teachers across the globe, which has been reported to surpass that of native English teachers (NETs), much controversy has been aroused globally, especially in the Asian context, over issues concerning the language proficiency of these Non-Native English Teachers (NNETs). Further commotion was fueled after the revelation of some of NNETs' unsatisfactory linguistic competence and/or knowledge in research and official language proficiency tests for teachers. This has led many to challenge whether NNETs are qualified as EFL/ESL teachers. Equally contentious in the literature are the formats, content, rationale, and difficulty of teacher language proficiency assessment. The focus of the present study, however, steers to a slightly new direction supported by the philosophy of greater practicality and usefulness for practitioners in ELT. This article reports on a qualitative study that delves into the relationship between teachers' general language proficiency (hereinafter referred to as TGLP) and their teaching effectiveness operationalized by learners' engagement. Classroom observations (of both NETs and NNETs), post-observation interviews with teachers and students, as well as interviews with highly proficient tertiary-level EFL students were conducted. The preliminary findings reveal that teachers' general linguistic competence plays an important role in ELT classrooms but once a proficiency threshold is met, higher language standards play a lesser role compared with other factors in contributing to teaching effectiveness. This article ends with implications for stakeholders in ELT as well as practical suggestions for further (quantitative) studies based on the present findings.