Light detection and ranging is widely used in science and industry. Over the past decade, optical frequency combs were shown to offer advantages in optical ranging, enabling fast distance acquisition with high accuracy. Driven by emerging high-volume applications such as industrial sensing, drone navigation, or autonomous driving, there is now a growing demand for compact ranging systems. Here, we show that soliton Kerr comb generation in integrated silicon nitride microresonators provides a route to high-performance chip-scale ranging systems. We demonstrate dual-comb distance measurements with Allan deviations down to 12 nanometers at averaging times of 13 microseconds along with ultrafast ranging at acquisition rates of 100 megahertz, allowing for in-flight sampling of gun projectiles moving at 150 meters per second. Combining integrated soliton-comb ranging systems with chip-scale nanophotonic phased arrays could enable compact ultrafast ranging systems for emerging mass applications.