Access to health information and services among women continues to be a major challenge in many communities globally. In recent years, there has been a growing interest in the potential of chatbots to address this information and access gap. We conducted interviews and focus group discussions with underserved women in urban India to understand their receptivity towards the use of chatbots for maternal and child health, as well as barriers to their adoption. Our findings uncover gaps in digital access and literacies, and perceived conflict with various responsibilities that women are burdened with, which shape their interactions with digital technology. Our paper offers insights into the design of chatbots for community health that can meet the lived realities of women in underserved settings.