let $\chi$ be a totally odd character of a totally real number field. in 1981, b. gross formulated a p-adic analogue of a conjecture of stark which expresses the leading term at s=0 of the p-adic l-function attached to $\chi\omega$ as a product of a regulator and an algebraic number. recently, dasgupta-darmon-pollack proved gross' conjecture in the rank one case under two assumptions: that leopoldt's conjecture holds for f and p, and a certain technical condition when there is a unique prime above p in f. after giving some background and outlining their proof, i will explain how to remove both conditions, thus giving an unconditional proof of the conjecture. if there is extra time i will explain an application to the iwasawa main conjecture which comes out of the proof, and make a few remarks on the higher rank case.