Daniel M. Ingram:
Hmmmm...
Well, the Brahma Viharas technically can be cultivated to the 3rd jhana for the first 3 and to the 4th jhana for Equanimity.
As to which chakra, I can see what you are getting at, but I would be more inclined to do something less progressive in some ways, at least were one to try to correlate this, meaning that I would actually put the first 3 in the heart chakra (4th), with compassion resonating at the 3rd chakra also, as much real heart-pain like resonance with suffering hits at the 3rd, and metta resonating just a bit at the 1st for exactly the security reason you mention, although viscerally most of them will hit at the heart chakra as a felt experience, at least so it happens for me.
Questions of chakras are going to come up more in the 2nd jhana aspect of each of these, as by the time you get to 3rd you are too wide and diffuse to localize that narrowly.
As to Equanimity, it is really going to be wider than the chakras for the same reason, but in its early, less developed aspect, it is going to be more 6th and 7th, at least for me.
Thoughts?
Thanks Daniel for the input,
I rethought the idea and looked for Maslow's hierarchy of needs and the chakras to see how they align...then it seems easier to include some phrasing that the Brahma Viharas leave out which was an obvious gap (celibate monks wishing sexual fulfillment for example)

maslow-revisited-the-hierarchy-of-chakras/ <---Cool article
I think you are correct where the jhanas come in...It gets complicated. I don't know if it correlates easily enough to do anything with.
I tend to experience body bliss, happiness, giddiness/2nd jhana in the stomach area but when I get to loving kindness it moves to the heart area. 3rd jhana/mental joy I kinda want to put at the third eye but you are right in that with the diffuseness I may just be intellectually forcing it there and even more so with Equinimity.
My original idea was a practice that was more inclusive and specific in well wishing that had a visceral energetic feel that could also move me thru the jhanas...hmmm... maybe too many birds, not enough of one stone.