Crowdsourcing linguistic phenomena with smartphone applications is relatively new. In linguistics, apps have predominantly been developed to create pronunciation dictionaries, to train acoustic models, and to archive endangered languages. This paper presents the first account of how apps can be used to collect data suitable for documenting language change: we created an app, Dialäkt Äpp (DÄ), which predicts users' dialects. For 16 linguistic variables, users select a dialectal variant from a drop-down menu. DÄ then geographically locates the user's dialect by suggesting a list of communes where dialect variants most similar to their choices are used. Underlying this prediction are 16 maps from the historical Linguistic Atlas of German-speaking Switzerland, which documents the linguistic situation around 1950. Where users disagree with the prediction, they can indicate what they consider to be their dialect's location. With this information, the 16 variables can be assessed for language change. Thanks to the playfulness of its functionality, DÄ has reached many users; our linguistic analyses are based on data from nearly 60,000 speakers. Results reveal a relative stability for phonetic variables, while lexical and morphological variables seem more prone to change. Crowdsourcing large amounts of dialect data with smartphone apps has the potential to complement existing data collection techniques and to provide evidence that traditional methods cannot, with normal resources, hope to gather. Nonetheless, it is important to emphasize a range of methodological caveats, including sparse knowledge of users' linguistic backgrounds (users only indicate age, sex) and users' self-declaration of their dialect. These are discussed and evaluated in detail here. Findings remain intriguing nevertheless: as a means of quality control, we report that traditional dialectological methods have revealed trends similar to those found by the app. This underlines the validity of the crowdsourcing method. We are presently extending DÄ architecture to other languages.