An $n$ component Brunnian Link is a link of $n$ components ($n \geq 3$)that is not the unlink, but such that if any one component is deleted the remaining $n-1$ components form an unlink.

We give a simple proof that Brunnian links of 3,4, and 5 components cannot be constructed out of perfect circles (ie geometrically round circles). The case $n=3$ was already known.