As the field of superconducting quantum computing advances from the few-qubit stage to largerscale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence (T1, T 2,echo > 20 µs) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips.