Similar to a design process for designing graphical user interfaces, conversation designers often apply an iterative design process by defining a conversation flow, testing with users, reviewing user data, and improving the design. While it is possible to iterate on conversation design with existing chatbot prototyping tools, there still remain challenges in recruiting participants on-demand and collecting structured feedback on specific conversational components. These limitations hinder designers from running rapid iterations and making informed design decisions. We posit that involving a crowd in the conversation design process can address these challenges, and introduce ProtoChat, a crowd-powered chatbot design tool built to support the iterative process of conversation design. ProtoChat makes it easy to recruit crowd workers to test the current conversation within the design tool. ProtoChat's crowd-testing tool allows crowd workers to provide concrete and practical feedback and suggest improvements on specific parts of the conversation. With the data collected from crowd-testing, ProtoChat provides multiple types of visualizations to help designers analyze and revise their design. Through a three-day study with eight designers, we found that ProtoChat enabled an iterative design process for designing a chatbot. Designers improved their design by not only modifying the conversation design itself, but also adjusting the persona and getting UI design implications beyond the conversation design itself. The crowd responses were helpful for designers to explore user needs, contexts, and diverse response formats. With ProtoChat, designers can successfully collect concrete evidence from the crowd and make decisions to iteratively improve their conversation design.