This study presents results from a randomized controlled trial involving 1,085 participants in Switzerland that have access to an E-bike, a car, and public transport. The participants' transport choices are monitored by means of a GPS-based tracking app. The treatment consists in a monetary incentive that approximates the main external costs and benefits associated with transport in the spirit of a Pigovian tax. This tax reduces transport-related external costs by 6.9\%, which corresponds to 78 Swiss francs per person and year (currently equivalent to 94 US dollars). The main underlying mechanism is a mode shift away from driving towards E-biking, public transport and walking. The results are primarily driven by individuals who own an S-pedelec with support up to 45 km/h, rather than users of the more common E-bikes that provide support up to 25 km/h. The pricing also induces a travel shift towards less congested time windows.