No. I am looking at the 2014 Form 990 filed with the IRS for the foundation. In part VII, compensation of officers and directors is listed. Chelsea Clinton’s salary is reported as zero. See https://www.clintonfoundation.org/sites/default/files/clinton_foundation_report_public_2014.pdf

So, unless someone comes up with credible evidence that the tax preparers for the Clinton Foundation committed an easily discoverable tax fraud, this assertion appears to be baloney.

From the FAQ from Clinton Foundation:

Do the Clintons receive any income or personal expense reimbursement from the Foundation?

No. President Clinton and Chelsea Clinton, who serve on the Board of Directors, do not take a salary from the Clinton Foundation and receive no funding from it. Secretary Clinton did not take a salary when she served on the Board of Directors.

Source: Frequently Asked Questions

The assertion in the question appears to be a variant of Clinton-related nonsense that appears from time to time. FALSE: Chelsea Clinton Made $900,000 Working for Her Parents