We present a practical and highly secure method for the authentication of chips based on a new concept for implementing strong Physical Unclonable Function (PUF) on field programmable gate arrays (FPGA). Its qualitatively novel feature is a remote reconfiguration in which the delay stages of the PUF are arranged to a random pattern within a subset of the FPGA's gates. Before the reconfiguration is performed during authentication the PUF simply does not exist. Hence even if an attacker has the chip under control previously she can gain no useful information about the PUF. This feature, together with a strict renunciation of any error correction and challenge selection criteria that depend on individual properties of the PUF that goes into the field make our strong PUF construction immune to all machine learning attacks presented in the literature. More sophisticated attacks on our strong-PUF construction will be difficult, because they require the attacker to learn or directly measure the properties of the complete FPGA. A fully functional reference implementation for a secure "chip biometrics" is presented. We remotely configure ten 64-stage arbiter PUFs out of 1428 lookup tables within a time of 25 seconds and then receive one "fingerprint" from each PUF within 1 msec.