The gemara (Sota 39) writes that R’ Elazar ben Shamu’a attributed his longevity to the fact that he never duchened without first saying a bracha. I would not blame you if you were not impressed. One is obligated to say a birchas hamitzvah before doing most mitzvos. Why would an Amora think that his special arichus yamim, his longer than normal life, should be attributed to the merit of his not messing up something so basic like saying a bracha before doing a mitzvah?
From here we see proof, says the GR”A (O.C. 128:30), that there is in fact no requirement to say a bracha before the mitzvah of birchas kohanim. It is certainly meritorious to do so, but it is not an obligation.
The question that begs asking is why this chiddush should be true: Why is the mitzvah of birchas kohanim different than any other mitzvah which requires a bracha before performing?
When I mentioned this issue to my son, he gave what I thought was a very good answer. The Nesivos in his commentary to the haggadah asks why it is that there is no bracha before the mitzvah of magid. He answers that you can’t make a bracha on a bracha. For example, there is no bracha on birchas hamazon because birchas hamazon itself is a bracha. What’s the lomdus, the reasoning, behind the Nesivos’ rule? The new edition has a nice footnote where they explain that the whole purpose of reciting a bracha is to give thanks and praise to Hashem. Were a person to preface that praise and thanks with an “asher kidishanu b’mitzvosav v’tzivanu…” it would defeat the whole point. A little kid can maybe get away with and saying, “My Mommy/Daddy told me I have to say thank you,” but an adult surely cannot. Kal v’chomer it would be improper to to approach Hashem saying, “I was commanded to say thank you, so here it is." We omit the birchas hamitzvah before we say the bracha of “Asher ga’alanu” (and R’ Shlomo Kluger already criticizes the fact that the Nesivos reduces magid to this bracha alone) and before we say “Birchas hamazon” because we want to recite those brachos and thanks Hashem as if there were no command to do so, as if we were motivated purely by our own sincerity. Shouldn’t the same should be true of birchas kohanim? (And I admit that at first I thought one could be mechaleik between a bracha to Hashem and the blessing of Klal Yisrael, but one second thought, I think my son is right.) To speak of “v’tzivanu,” the burden of fulfilling a command, seems to undermine the idea of “l’vareich as amo Yisrael b’ahavah,” the feeling of love for Klal Yisrael that the bracha is supposed to express and which the kohen is trying to convey
I saw a different hesber from R’ Zecharya Tubi, Rosh Kollel in KBY. A kohen only is obligated to duchan if the tzibur calls him to do say, based on the pasuk, “Amor lahem.” Based on this, the Pri Megadim writes that the tzibur has a right to be mochel on birchas kohanim if they choose to do so. The Rashba in his teshuvos has a yesod that one never recites a bracha on a mitzvah which is subject to mechila. For example, one would not recite a bracha on the mitzvah of tzedaka because the recipient could always be mochel receipt of the money. QED, the mitzvah of birchas kohanim also does not require the recitation of a bracha.