City officials fear development of a peak just to the west of the "H" in the sign would encroach on the postcard-like scene.
The 1,820-foot Cahuenga Peak is where Howard Hughes once planned to build a love nest for actress Ginger Rogers.
But a group of Chicago investors who four years ago purchased the land from Hughes' estate are eyeing the 138 acres of the ridge as a place to nestle in five luxury estates.
That has prompted a hasty campaign by city leaders and conservationists to raise $6 million they think they need to buy back Cahuenga Peak and turn it into an extension of nearby Griffith Park.
So far they have amassed $3.1 million from various sources.
Representatives for the Chicago owners said Thursday that they are "open" to a bid from the city, though the investors are preparing to draw up their own development plans. They said previous talks with the city about the mountaintop fell apart. No current asking price has been set.
From its top, a spectacular 360-degree panorama of the Los Angeles Basin and the San Fernando Valley unfolds for hikers who manage to climb the road-less peak just east of the Cahuenga Pass.
Though building homes on the rugged mountain would be a challenge, officials said they were concerned about the peak's future because of the boom in recent years of luxury home construction across even the steepest areas of the Hollywood Hills.
"With modern engineering techniques, there's no such thing as an un-buildable lot," said Hollywood-area City Councilman Tom LaBonge, who is leading the campaign to buy the peak.
"It's been sitting there for a long time. We kind of forgot about it. I was as surprised as anybody to find out we didn't already own that parcel. It looks like we do, but we don't."
Authorities say that Hughes, the aircraft builder turned filmmaker, acquired the land in the 1930s. That's when he drove Rogers up the mountainside and pledged to construct her a house there.
"He said, 'Sweetheart, see the city below you? I'm going to build a house here for you,' " said Rad Sutnar, a consultant working for the landowners who has studied the site's history.
In a 1991 television interview, Rogers mentioned Hughes' house plans as a reason she never married the eccentric tycoon.
"I knew what he wanted from me. He wanted to take me and lock me up in a hilltop house and never let me see anyone," Rogers said.
"That's exactly what he did to [actress] Jean Peters. He locked her up. I could tell how resentful he was of anyone coming close to us in conversation."
Hughes' relationship with Rogers didn't last. But the property remained in the Hughes trust for decades.
The investors, working through a partnership called Fox River Land Co., purchased Cahuenga Peak from Howard Hughes Properties Ltd. in 2002 for $1,675,000, according to Los Angeles County property records.
A year later, the investors divided their holdings into five pieces under a partnership called Hollywood Hills LLC.