The ongoing COVID-19 pandemic has raised concerns for many regarding personal and public health implications, financial security and economic stability. Alongside many other unprecedented challenges, there are increasing concerns over social isolation and mental health. We introduce \textit{Expressive Interviewing}--an interview-style conversational system that draws on ideas from motivational interviewing and expressive writing. Expressive Interviewing seeks to encourage users to express their thoughts and feelings through writing by asking them questions about how COVID-19 has impacted their lives. We present relevant aspects of the system's design and implementation as well as quantitative and qualitative analyses of user interactions with the system. In addition, we conduct a comparative evaluation with a general purpose dialogue system for mental health that shows our system potential in helping users to cope with COVID-19 issues.