We measure the clustering of Lyman Alpha Emitting galaxies (LAEs) selected from the One-hundred-square-degree DECam Imaging in Narrowbands (ODIN) survey, with spectroscopic follow-up from Dark Energy Spectroscopic Instrument (DESI). We use DESI spectroscopy to optimize our selection and to constrain the interloper fraction and redshift distribution of our narrow-band selected sources. We select samples of 4000 LAEs at z = 2.45 and 3.1 in 9 sq.deg. centered on the COSMOS field with median Lyα fluxes of ≈ 10-16 erg s-1 cm-2. Covariances and cosmological inferences are obtained from a series of mock catalogs built upon high-resolution N-body simulations that match the footprint, number density, redshift distribution and observed clustering of the sample. We find that both samples have a correlation length of r 0 = 3.0 ± 0.2 h-1 Mpc. Within our fiducial cosmology these correspond to 3D number densities of ≈ 10-3 h3 Mpc-3 and, from our mock catalogs, biases of 1.7 and 2.0 at z = 2.45 and 3.1, respectively. We discuss the implications of these measurements for the use of LAEs as large-scale structure tracers for high-redshift cosmology.