Why does the Torah see fit to repeat (See Sifsei Chachamim) that the chest goes to the Kohanim?
Rashi: To teach that they acquire it only after the Chelev is burned on the Mizbe'ach. 1
Moshav Zekenim: This is when the Chelev is intact, but if it became Tamei or was lost, the Kohen acquires Chazah v'Shok through Zerikas ha'Dam - "v'Dam Zevachecha Yishafech