Raman spectra of hexagonal close-packed iron (varepsilon-Fe) have been measured from 15 to 152 gigapascals by using diamond-anvil cells with ultrapure synthetic diamond anvils. The results give a Gruneisen parameter gamma(0) = 1.68 (+/-0.20) and q = 0.7 (+/-0.5). Phenomenological modeling shows that the Raman-active mode can be approximately correlated with an acoustic phonon and thus provides direct information about the high-pressure elastic properties of iron, which have been controversial. In particular, the C(44) elastic modulus is found to be lower than previous determinations. This leads to changes of about 35% at core pressures for shear wave anisotropies.