Qualitative analysis is a challenging, yet crucial aspect of advancing research in the field of Human-Computer Interaction (HCI). Recent studies show that large language models (LLMs) can perform qualitative coding within existing schemes, but their potential for collaborative human-LLM discovery and new insight generation in qualitative analysis is still underexplored. To bridge this gap and advance qualitative analysis by harnessing the power of LLMs, we propose CHALET, a novel methodology that leverages the human-LLM collaboration paradigm to facilitate conceptualization and empower qualitative research. The CHALET approach involves LLM-supported data collection, performing both human and LLM deductive coding to identify disagreements, and performing collaborative inductive coding on these disagreement cases to derive new conceptual insights. We validated the effectiveness of CHALET through its application to the attribution model of mental-illness stigma, uncovering implicit stigmatization themes on cognitive, emotional and behavioral dimensions. We discuss the implications for future research, methodology, and the transdisciplinary opportunities CHALET presents for the HCI community and beyond.