"I gotta tell the grandchildren what it's supposed to look like," said Bernice Kruszewski in puzzlement. "But what is it supposed to look like?"

Accompanied by her friend, Margaret O'Hara, she warily circled the newest thing in Chicago.

When they looked at it from the north side, O'Hara thought she might know what it was supposed to be: "A lighthouse," she suggested.

Kruszewski wasn't so sure. "A haunted house," she responded.

They were staring at a 29-foot-high white Stonehenge-like object that, together with three other associated shapes, now rises without much warning out of a stretch of sidewalk at Clark and Randolph streets in the heart of the downtown Loop.

The assemblage is "Monument With Standing Beast," by Jean Dubuffet, and was unveiled and dedicated today at a ceremony that rightly hailed Chicago's world reputation as a place where monumental public sculpture fits right in. Dubuffet's lively new work joins that of Picasso, Miro', Oldenburg, Calder and Chagall, among many others, as part of the multimillion-dollar collection on view here outside dozens of buildings throughout the Loop.

The arresting new Dubuffet, taken from the 85-year-old artist's "Hourloupe" cycle of paintings, is of painted fiberglass over a steel skeleton. It was fashioned by Dubuffet's longtime assistant, Richard Dhoedt, in Dhoedt's studio outside Paris, and shipped here earlier this year. It is now installed in front of the new State of Illinois Building, an unusually shaped steel and glass office tower. Designed by Helmut Jahn, the unfinished building boasts a 13-story enclosed atrium and has drawn stares and comment for months.

The Dubuffet seems in harmony with the ambitious aims of the new building. The work of art is meant to appeal to meditation, spiritual stimulation and visual excitement, according to a press release. Its white sides seem likely to appeal as well to graffiti artists and mountain climbers.

At the dedication, Illinois Gov. James R. Thompson seemed aware of the apparent vulnerability of the new work. "May vandals never touch it," he told a crowd of dignitaries. "May children ever touch it." The sculpture, insured for $1 million, was donated by the Leonard J. Horwich Family Foundation, the Graham Foundation for Advanced Studies in the Fine Arts and an anonymous donor.

Once the dedication was out of the way and the governor had taken his crowd for a peek at the unfinished state office building for which the Dubuffet was donated, casual onlookers made their first acquaintance with the new work.

Among them were O'Hara and Kruszewski. Veteran Cook County employes, the two women have seen and heard many strange things in their years of public service. But never anything quite like this, the newest thing in Chicago.

So after finding the north side of the sculpture to resemble a lighthouse or a haunted house, they walked around to the southeast side of the collection of shapes and took another look.

The high, white slab on the north now seemed less important to worry about. Something else was to be seen.

A 15-foot-tall shape stood before them.

"A rearing horse," said O'Hara with more confidence. "See the feet up in the air like that?"

"I do . . ." said Kruszewski. "It does look like a horse." A head, a mane, two legs pawing the air, a vertical body.

White, with bold black outlines painted along the corners -- perhaps it had been jigsawed by a giant from a huge slice of cream cheese that had gone slightly tacky, then congealed.

"I think I can't really tell the grandchildren," Kruszewski said. "Maybe I'll have to do a drawing for them."

"But what's all of it together supposed to look like?" another passerby mused. He was staring at the 29-foot-high slab-kind-of-thing that stood behind the sort-of-horse. No one answered him readily, so the passer-by went looking for reactions.

He found Patrick Goldwyre standing to the west of the sculpture. Goldwyre had a big grin on his face. "Can you imagine? People gonna catch planes and come here from everywhere just to look at that thing!"

But what does the sculpture look like? the passerby asked.

"Ssss-ssss-ssss," Goldwyre hissed in merriment through his teeth. "You don't expect me to answer a damn fool question like that, do you?"