A time-bin qubit is a promising candidate qubit for advanced quantum information processing systems operating over optical fibers or integrated quantum photonic circuits. However, the single- and two-qubit operations of time-bin qubits have been largely unexplored compared with those of polarization qubits. Here, I present a simple scheme for implementing a basic two-qubit operation, namely an ``entangling'' operation of two independent time-bin qubits, based on Hong-Ou-Mandel quantum interference in a high-speed $2\ifmmode\times\else\texttimes\fi{}2$ optical switch. With the proposed scheme, the formation of a time-bin entanglement was confirmed experimentally.