"We are so excited to introduce these amazing new Quinoa Bowls that we wanted to do something big, maybe even a little crazy," said Chief Marketing Officer Kevin Mayer.
The promotion ends on Labor Day (note the pun) and only one winner will be announced.
"BJ's thinks that Quinoa could be a really great baby name, so who knows, maybe it will start a trend," Mayer told CNBC.
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For those who are not expecting a baby this summer, there is still a way to get in on the action. Anyone who changes his or her name to Quinoa on Twitter until July 6 will get a $10 off $35 coupon to the restaurant chain.
BJ's Restaurants operate 163 restaurants in 20 states including Arizona, California and New York. The new menu items that inspired the promotion are the "Roasted Chicken with Spinach Quinoa Bowl" and the "Roasted Salmon Quinoa Bowl." Both are options on the lighter menu which includes items under 795 calories.
The winner will receive a $10,000 gift card valid for use at any BJ's restaurant. Parents must provide a copy of the baby's birth certificate and submit it by October 21, 2015 by email or snail mail.