Robert W. Wilson, a retired investor and philanthropist who has donated hundreds of millions of dollars to environmental charities, has created what appears to be an unprecedented fund-raising challenge.

To help a relatively small environmental charity in Arlington, Va., Mr. Wilson, 82, says he will match, dollar-for-dollar, the largest gift the group can raise by the end of its fiscal year on September 30 — with no upper limit on the amount he will give to fulfill his part of the bargain.

The “Wilson Challenge,” as it is called, will benefit Rare, an Arlington, Va., organization that works to promote conservation around the world. The gift is Mr. Wilson’s first to the organization, which has a staff of 65, 35 of whom work overseas, and a budget of $9-million.

In addition to placing no limit on the amount he is willing to give, Mr. Wilson had another stipulation for the gift he will ultimately match: It must be paid in full by September 30.

Today Rare announced it has a taker: Longtime conservation advocate Wendy J. Paulson, Rare’s board chair and the wife of former Treasury Secretary Henry M. Paulson, says she will donate $6.1-million to the challenge, which would generate $12.2-million with Mr. Wilson’s match.

But Rare is hoping to get other “bids” that are even higher before the challenge comes to an end.

If such a gift comes through, Mr. Wilson is unlikely to have any trouble matching it: He has already given $100-million to each of four other environmental charities.

(Read The Chronicle’s profile of Mr. Wilson’s unusual approach to philanthropy.)