  Traditionally, quantum entanglement has played a central role in foundational
discussions of quantum mechanics. The measurement of correlations between
entangled particles can exhibit results at odds with classical behavior. These
discrepancies increase exponentially with the number of entangled particles.
When entanglement is extended from just two quantum bits (qubits) to three, the
incompatibilities between classical and quantum correlation properties can
change from a violation of inequalities involving statistical averages to sign
differences in deterministic observations. With the ample confirmation of
quantum mechanical predictions by experiments, entanglement has evolved from a
philosophical conundrum to a key resource for quantum-based technologies, like
quantum cryptography and computation. In particular, maximal entanglement of
more than two qubits is crucial to the implementation of quantum error
correction protocols. While entanglement of up to 3, 5, and 8 qubits has been
demonstrated among spins, photons, and ions, respectively, entanglement in
engineered solid-state systems has been limited to two qubits. Here, we
demonstrate three-qubit entanglement in a superconducting circuit, creating
Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with
quantum state tomography. Several entanglement witnesses show violation of
bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first
step of basic quantum error correction, namely the encoding of a logical qubit
into a manifold of GHZ-like states using a repetition code. The integration of
encoding, decoding and error-correcting steps in a feedback loop will be the
next milestone for quantum computing with integrated circuits.
