We suggest indirect excitons in 2D semiconductor heterostructures as a platform for realization of a bosonic analog of the Bardeen-Cooper-Schrieffer superconductor. The quantum phase transition to a biexcitonic gapped state can be controlled in situ by tuning the electric field applied to the structure in the growth direction. The proposed playground should allow one to go to strongly correlated and high-temperature regimes, unattainable with Feshbach resonant atomic gases.PACS numbers: 71.35. Lk, 34.50.Cx, 67.10.Ba, 74.10.+v The phenomenon of resonant pairing lies at the heart of superconductivity in metals. Here Cooper pairs of fermionic particles -electrons, can Bose-Einstein condense to carry electric charge without dissipation. In-depth study of this scenario, commonly known as Bardeen-CooperSchrieffer (BCS) theory, has been performed by using the technique of Feshbach resonances (FR's) in ultracold atomic gases. In Fermi gases this technique has allowed for observation of a crossover from a BCS-like state made of spatially overlapping pairs of atoms to a BoseEinstein condensate (BEC) of tightly bound diatomic molecules [1][2][3][4][5]. This so-called BCS-BEC crossover has become a paradigm of the many-body physics, sharing important analogies with high-temperature superconductivity [6] and neutron stars [7][8][9].A natural idea expounded in a series of papers [10] has been to apply the same FR technique to degenerate Bose gases. It has been shown that in the case of bosons the smooth crossover is replaced by a thermodynamically sharp phase transition from a coherent mixture of atoms and molecules to a pure molecular superfluid [11]. The latter is distinguished by the absence of atomic offdiagonal long-range order and gapped atomic excitations. Though being of great fundamental interest on its own right, until now this research has not met its applicationoriented counterpart in the physics of solid state. Moreover, experimental attempts to realize a unitary Bose gas of atoms did not succeed. This is due to coalescence of three and more atoms (few-body recombination) [12,13] and mechanical instability when approaching the resonance on the attractive side [14].In this Letter we propose a new setting for study and manipulation of resonantly paired bosonic superfluids. Bosonic quasiparticles we consider are indirect excitons in biased semiconductor heterostructures. Our excitonic analog of BCS is expected to be stable across the whole range of scattering lengths. The scattering length of the excitons can be conveniently tuned by the bias electric field. A distinct feature of an indirect exciton is a large dipole moment oriented perpendicularly to the structure plane. In the system under consideration an interplay between the long-range dipolar repulsion and the resonant interaction may result in formation of a fragmented biexcitonic supersolid. This new strongly correlated state of bosonic matter would be robust to fluctuations of all kind which usually spoil superconductivity in low dimensions. In transitio...