The potential usage scenarios of dialogue systems will be greatly expanded if they are able to collaborate more creatively with humans. Many studies have examined ways of building such systems, but most of them focus on problem-solving dialogues, and relatively little research has been done on systems that can engage in creative collaboration with users. In this study, we designed a tagline co-writing task in which two people collaborate to create taglines via text chat, created an interface for data collection, and collected dialogue logs, editing logs, and questionnaire results. In total, we collected 782 Japanese dialogues. We describe the characteristic interactions comprising the tagline co-writing task and report the results of our analysis, in which we examined the kind of utterances that appear in the dialogues as well as the most frequent expressions found in highly rated dialogues in subjective evaluations. We also analyzed the relationship between subjective evaluations and workflow utilized in the dialogues and the interplay between taglines and utterances.