We present a flip-chip architecture for an array of coupled superconducting qubits, in which circuit components reside inside individual microwave enclosures. In contrast to other flip-chip approaches, the qubit chips in our architecture are electrically floating, which guarantees a simple, fully modular assembly of capacitively coupled circuit components, such as qubit, control, and coupling structures as well as reduced crosstalk between the components. We validate the concept with a chain of three nearest neighbor coupled generalized flux qubits in which the center qubit acts as a frequency-tunable coupler. Using this coupler, we demonstrate a transverse coupling on/off ratio≈50, zz−crosstalk ≈0.7 kHz between resonant qubits and isolation between the qubit enclosures>60 dB.