Abstract We present the median-stacked Lyman-α (Lyα) surface brightness profiles of 968 spectroscopically selected Lyα emitting galaxies (LAEs) at redshifts 1.9 < z < 3.5 in the early data of the Hobby-Eberly Telescope Dark Energy Experiment. The selected LAEs are high-confidence Lyα detections with high signal-to-noise ratios observed with good seeing conditions (point-spread function FWHM <1.″4), excluding active galactic nuclei. The Lyα luminosities of the LAEs are 10^42.4–10⁴³ erg s⁻¹. We detect faint emission in the median-stacked radial profiles at the level of ( 3.6 ± 1.3 ) × 10 − 20 erg s − 1 cm − 2 arcsec − 2 from the surrounding Lyα halos out to r ≃ 160 kpc (physical). The shape of the median-stacked radial profile is consistent at r < 80 kpc with that of much fainter LAEs at 3 < z < 4 observed with the Multi Unit Spectroscopic Explorer (MUSE), indicating that the median-stacked Lyα profiles have similar shapes at redshifts 2 < z < 4 and across a factor of 10 in Lyα luminosity. While we agree with the results from the MUSE sample at r < 80 kpc, we extend the profile over a factor of two in radius. At r > 80 kpc, our profile is flatter than the MUSE model. The measured profile agrees at most radii with that of galaxies in the Byrohl et al. cosmological radiative transfer simulation at z = 3. This suggests that the surface brightness of a Lyα halo at r ≲ 100 kpc is dominated by resonant scattering of Lyα photons from star-forming regions in the central galaxy, whereas at r > 100 kpc, it is dominated by photons from galaxies in surrounding dark matter halos.