The food giant Unilever thinks not. And it is suing Hampton Creek, a start-up company making an eggless spread that tastes like mayonnaise, accusing it of false advertising and fraud.

Hampton Creek, whose investors include Bill Gates, the Hong Kong billionaire Li Ka-shing and prominent venture capitalists, replaces eggs with yellow peas in its spread, which is called Just Mayo.

In its lawsuit, Unilever contends that Just Mayo is denting sales of its popular mayonnaise products, known as Hellmann’s in the East and Best Foods west of the Rockies.

Andrew Zimmern, a television chef who is a fan of Just Mayo, started a petition online at Change.org on Sunday, asking Unilever to “stop bullying” small companies. By Monday morning, it had more than 10,000 supporters.