Now, a major retrospective of her work is opening there.
It's her first in the United States. The timing is a nice present for Hurtado, who will turn 100 this year.
For most of her life, Hurtado painted and drew, and few people knew of her work.
Now they do.
She was born in Venezuela, emigrated, lived in the avant-garde art world, married three times and had a family. Her evolving styles have come to focus on our ecology - and her message is so direct she laughs at the irony:
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"I think-- clean things up!" laughed Hurtado. "Simple!"
The scope of Hurtado's work in the show starts in the '40s, but one of the pieces was completed only weeks ago. She was featured in a show of emerging artists less than two years ago; and since then, she has gone global.
"She just had a show at the Serpentine in London," said Michael Govan, LACMA director. "And that was the occasion for this show. They gathered the works, coming back home to Los Angeles, and so we literally parted the way at LACMA to create space in our galleries for this show."
A fellow Venezuelan stopped by the show opening night with his congratulations - the L.A. Philharmonic's maestro, Gustavo Dudamel.
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"To have a beautiful piece of Venezuela here in Los Angeles with Luchita - it's amazing. I'm very proud, really," said Dudamel.
The title of the show is "I Live, I Die, I Will Be Reborn." It appears Hurtado only has time for living.
"I'm still working. Yes I am. It's like living, you know. Your life is your life," said Hurtado. "And I choose to spend my days painting."
The exhibit is open at LACMA through May 3.