According to the Star-K website, quinoa is Kosher for Passover. However, because it is often grown and processed in proximity to grains that are not, it “should only be accepted with reliable Kosher for Passover supervision.”
This year, Star-K has certified that Lot code 3.01.14 k of Ancient Harvest brand quinoa is Kosher for Passover. For more information, see the Star-K website. The Quinoa Corporation website has published a list of stores where this special lot number (they list it as #030114K) is available on their website.