We have succeeded in coupling two solid-state qubits and observing quantum coherent dynamics of such a system. Each qubit is a Cooper-pair box whose quantum states are manipulated by means of pulse technique. Coupling of the two qubits is done by using a small on-chip capacitor. For read-out of the state of each qubit, we use probe electrodes connected to the Cooper-pair boxes through resistive tunnel junctions. Quantum coherent oscillation of the two-qubit charge states results in the oscillation of the probe currents. The observed "beatings" as well as avoided level crossing in the energy spectrum is a direct evidence for the interaction of the two qubits. Although we could not measure the amount of entanglement directly, our simulations based on the experimental data show that during quantum evolution the qubits remain entangled most of the time. A straightforward continuation of this experiment is a demonstration of conditional gate operation, a prototype of a solid-state quantum logic gate.