A sign of a possible peak in the oil boom has emerged.

Lois Weiss of the New York Post reports that the Abu Dhabi Investment Council is negotiating an $800 million deal for a 75 percent stake in the Chrysler Building.

Buying trophy properties can be a bad omen. In the 1980s, amid fears that Japan would overtake the United States as the leading economic power, Japanese investors bought properties like the Pebble Beach golf course, the Sony movies studio, and Rockefeller Center. It was the pride before the fall.

The Persian Gulf sovereign wealth funds have been more agile, more sophisticated investors, taking stakes in businesses from Barneys to Sony. Late last year, the Abu Dhabi Investment Council's larger sister, the Abu Dhabi Investment Authority took a 4.9 percent stake in Citigroup for $7.5 billion, to become the bank's largest shareholder.

But with hundreds of billions of oil dollars to invest, and with oil headed for $150 a barrel, it may be a harder temptation to resist a famous name.

Since 1930, the Chrysler Building has been a major symbol of Manhattan, defining its Midtown skyline.

The talks come as the sale of another famous Manhattan building, the General Motors Building, has just closed. Mort Zuckerman, along with Goldman Sachs, Morgan Stanley, and funds based in Qatar and Kuwait bought that building for $2.9 billion.

Indeed, there may be a wave of deals involving Manhattan landmarks. Daniel Pimlott of the Financial Times reports that the Sorgente Group, an Italian family-run property investor, is in talks to take the largest stake in the Flatiron Building in a deal that could eventually transform it into a luxury hotel.

In the Chrysler deal, Weiss says the 75 percent stake would be sold by TMW, which is the German arm of an Atlanta-based investment fund. Tishman Speyer Properties owns the other 25 percent.

It may be unfair to assume that with oil prices sky-high, Persian Gulf funds are losing their investment focus.

Dubai International Capital recently walked away from talks to buy 50 percent of Liverpool Football Club, for nearly $400 million, even though its chief executive is a huge fan of the soccer team.

And the Abu Dhabi Investment Authority, for one, is becoming a more conservative investor, according to an article by Emily Thornton and Stanley Reed in BusinessWeek.

The fund, with an estimated $875 billion in assets, is cutting its investments in hedge funds and putting more money into index funds.

And the recent history of Japan is very much on the minds of the fund's managers.

"When people ask what keeps you awake at night, it is trying to avoid investing massively in another Japan in 1990," Jean-Paul Villain, a French executive in charge of strategy at the fund, told BusinessWeek.