The measurement of coronal fields has in the past generally been restricted to the field strength or to only some of the components of the magnetic vector. We present here a technique for measuring the full magnetic vector near the base of the solar corona. As an application we report on observations of a developing active region with ongoing magnetic flux emergence. The data allow the first measurement of the 3-D structure of magnetic loops. They also provide the first detection of an electric current sheet located near the base of the solar corona. Such current sheets or tangential discontinuities of the coronal magnetic field have long been thought to be a major source of coronal heating.