We describe a new approach to precision NMR with hyperpolarized gases designed to mitigate NMR frequency shifts due to the alkali spin exchange field. The electronic spin polarization of optically pumped alkali atoms is square-wave modulated at the noble-gas NMR frequency and oriented transverse to the DC Fourier component of the NMR bias field. Noble gas NMR is driven by spin-exchange collisions with the oscillating electron spins. On resonance, the time-average torque from the oscillating spin-exchange field produced by the alkali spins is zero. Implementing the NMR bias field as a sequence of alkali 2π-pulses enables synchronization of the alkali and noble gas spins despite a 1000-fold discrepancy in gyromagnetic ratio. We demonstrate this method with Rb and Xe, and observe novel NMR broadening effects due to the transverse oscillating spin exchange field. When uncompensated, the spin-exchange field at high density broadens the NMR linewidth by an order of magnitude, with an even more dramatic suppression (up to 70x) of the phase shift between the precessing alkali and Xe polarizations. When we introduce a transverse compensation field, we are able to eliminate the spin-exchange broadening and restore the usual NMR phase sensitivity. The projected quantum-limited sensitivity is better than 1 nHz// √ Hz.The ability to produce highly magnetized noble gases via spin-exchange collisions with spin-polarized alkali atoms [1] has greatly impacted scientific studies of magnetic resonance imaging [2], high-energy nuclear physics with spin-polarized targets [3], and chemical physics [4]. Applications in precision measurements began with NMR gyros [5] and have continued with fundamental symmetry tests using multiple cell free induction decay [6], dual-species masers [7,8], selfcompensating co-magnetometers [9], NMR oscillators [10], and free spin-precession co-magnetometers [11][12][13][14].Some of these approaches [5, 9-11, 14] take advantage of enhanced NMR detection by the embedded alkali magnetometer. The alkali and noble-gas spin ensembles experience enhanced polarization sensitivity due to the Fermi-contact interaction during collisions between the two species. The effective Fermi-contact fields experienced by the two species arewhere S, K are the electron and nuclear spin operators, n S , n K the atomic densities, µ K the nuclear magnetic moment of the noble gas, µ B the Bohr magneton, and the atomic g-factor g ≈ 2. The frequency-shift enhancement factor κ [15,16] was recently measured to be 493 ± 31 [17] for RbXe. Thus the detected NMR field B SK is ∼500× larger for the embedded magnetometer than for any external sensor. This seemingly decisive advantage comes with the cost of similarly enhancing the B KS field due to the spin-polarized alkali atoms, 190 µG at 2n S S = 10 13 cm −3 . In typical longitudinally polarized NMR this field produces large frequency shifts of order 0.1 Hz. One approach for mitigating this effect is to compare two Xe isotopes [5,11], for which the enhancement factors are equal to about 0....