Chikuba no tomo is a phrase I learned a long time ago while randomly browsing through a kanji dictionary (way back when I was still working on kanji like 竹 (chiku, take). Browsing through kanji dictionaries, incidentally, is a GREAT way to learn phrases that nobody says any more.
A 竹馬の友 is a childhood friend. I've had mild success with saying things like 竹馬の家, but more for being amusing, than for being correct in my usage.
I only recently learned the origin of the phrase, however, in a conversation with one of the women who runs the vegetable stand in my neighborhood. See, for along time, I had mistakenly imagined the ば in ちくば、as this kanji： 場 which led me to believe that the 竹場 was a place of bamboo, which I imagined to be a tiny village, reminiscent of everyone's childhood home. Yay, ethnic stereotypes!
The real version, 竹馬, actually means bamboo horsey, and can be alternately read as たけうま, which is a game that Japanese children used to play a lot, and still play sometimes, probably as part of an organized, "Don't Forget Your Culture Day" at school. It consists of making tall stilts out of bamboo and running around on them. They might have たけうま races now, or some kind of competition, but for little kids, I'm sure the thrill of being taller and on stilts was enough for them to just frolic for hours. So, a friend with whom you engaged in bamboo horsey, and therefore, obviously a childhood friend, is your 竹馬の友。