Ms Hills stood on the platform and spoke - for the first time with passion, in the opinion of those who know her - about the new North American Free Trade Agreement (Nafta).
Only a short time before the convention, she had clinched a deal with Mexico, opening a potentially vast new market of 80 million consumers to US companies. A rare, brilliant smile of victory crossed her face as she enumerated the benefits to cheering delegates, many of whom only half understood what she was talking about.
Such is the life of a chief trade negotiator, a US cabinet official who toils on policy details that go largely unnoticed in the grand scheme of things.
Ms Hills has been at this work for four gruelling years. Now she has another chance to accomplish the seemingly impossible and secure a deal on agriculture with Europe before the US elections. This, in turn, will allow President Bush to announce that the historic and elusive Uruguay Round of trade liberalisation talks is at last moving to completion.
It is a long shot, with only a small window of opportunity over the next few weeks. But if Europe and the US agree, it will be the crowning achievement in the long, distinguished career of a woman who has served in two administrations.
It is doubtful, however, that the public will ever hear her talk about it. She does not give interviews for personal profiles. Unlike her predecessors, she does not chat up the press unless it is in the line of duty. In short, Ms Hills is all business.
Slender, reserved and with the air of a no-nonsense law professor, she is a stickler for detail and playing by the rules. Indeed, she is often accused by her European counterparts of being too rigid. Privately, EC officials complain that Ms Hills never lightens up, unlike her immediate predecessor, Clayton Yeutter, and the legendary US trade negotiator Robert Strauss, who was known for having a bourbon with the boys in the wee small hours of trade negotiations. This was his way of clinching deals.
Ms Hills is a different person altogether. One European described her as a negotiator with an iron fist in a velvet glove. She herself took great umbrage at a remark from one southern senator that she was a 'steel magnolia', a woman who looked soft but talked a tough game in her mission to 'pry open foreign markets' for US goods.
The Bush Administration often seemed to undercut Ms Hills's efforts by failing to put her in the spotlight, most notably at the Group of Seven economic summit in Houston, where the Uruguay Round was a major topic of discussion. Until the last, Ms Hills was not even invited to come, and when she did arrive, she was relegated to a secondary role. In the opinion of many of her supporters, this sent the wrong message to Europe and Japan.
None the less, she has come into her own in recent months with the successful deal on the Nafta - a 900-page agreement that must still be ratified by the US Congress. It is the key achievement in the Bush Administration's strategy to build regional trading houses while it continues to negotiate on the Uruguay Round. Indeed, many professionals believe that if Europe moves forward on agriculture, it will be in response to the threat of a US-dominated regional American trading centre that stretches from Alaska to Argentina. There is the grave fear that this market, much larger than the European Community and the Efta nations combined, would restrict access by Europeans, Asians and others in a drive to become the dominant trading centre.
Ms Hills, however, has always spoken in the measured tones of a free marketeer. Since taking office at the beginning of the Bush Administration, she has preached this gospel and adhered to it assiduously throughout long and tortuous negotiations. These have embraced the unenviable task of implementing the US Super 301 trade legislation, which was meant to punish countries with closed markets.
She manoeuvred through this minefield with great skill, avoiding all-out trade wars but still forcing Japan, Korea and the EC to open their markets in key industries. These successes included a dollars 2bn telecommunications agreement with Korea, wine and corn gluten feed deals with the EC and trade agreements with seven of the 12 independent republics of the former Soviet Union.
All this has required non-stop travel to the key countries in endless rounds of talks on the minutiae of issues. These have often taken place in the glare of publicity, which can harden positions. Ms Hills is good in this arena. She trained for the role - a US special trade representative with ambassadorial rank - as a high-powered lawyer in Washington and California. She also served in the Ford Administration as secretary of the Department of Housing and Urban Development, becoming only the third US woman to hold a cabinet-level position. In 1976, Time magazine named her as one of its 10 women of the year.
She has done all this while raising a family of four children and maintaining an active social life with her husband Roderick Hills, a former high US official. Ms Hills gains high marks from her friends for never missing an important school engagement involving her children, even if it meant taking a 15-minute break from a White House meeting to make an appearance.
In her role as mother, as in her role as cabinet official, she wields a firm hand. It was the relentless pursuit of a Uruguay Round solution that kept her in the administration last year when, in near-despair over the breakdown of the talks, she was tempted to resign.
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