"Angie Tribeca's" all-star roster of guest actors isn't just for show: Chris Pine and Natalie Portman add an extra layer of satire to the smartest dumb comedy on TV — and are damn funny to boot.

There’s a story about making “Angie Tribeca” that’s stuck with me. When Jon Hamm signed on for a guest role in the Season 2 premiere, he knew what he was in for: one scene, one line, three words. His character walked into a room, said “See you around,” and left. That’s it. That’s all he had to do. So…easy gig, right?

Not exactly.

“They brought him in at 7 a.m., and just before lunch, we rehearsed with him,” co-star Jere Burns said at a PaleyFest screening last April. “He just sat in his little trailer until we rehearsed. Then, after we rehearsed, we broke for lunch. We didn’t shoot him until after lunch. He could not have been nicer. Most actors, no matter who you are, you’re like, ‘This is so annoying. I have three words. I’ve been waiting around for seven hours.’ He could not have been more pleasant.”

“It’s like LeBron James coming to play for your team and just not giving him the ball,” Hayes MacArthur said.

But that was the joke, and everyone knew it. The writers knew it, Hamm knew it, and everyone on “Angie Tribeca” knows it during every moment of their brilliant spoof on cop shows. It’s so ridiculous, so unexpected, and so stupid it’s hysterical.

READ MORE: How Rashida Jones Changed Everything to Make ‘Angie Tribeca’ Perfect

Hamm’s cameo was just one of many, many, many celebrity guest spots in “Angie Tribeca,” dating back to everyone’s dream guest star, Bill Murray(!) in Season 1, and including Lisa Kudrow, Adam Scott, Keegan-Michael Key, Maya Rudolph, IndieWire contributor James Franco, and more throughout the first 20 episodes.

Such inclusions have already become a proud tradition that doubles as subtle satire: Police procedurals need a steady influx of fresh talent to fill new roles in each “case of the week,” leaving plenty of opportunities for famous faces to pop in for a quick ratings grab Emmy grab guest appearance. For example, look at how NBC promoted Robin Williams in an ad for his role in “Law & Order: SVU.” (And yes, he was nominated for an Emmy.)

READ MORE: Rashida Jones Says ‘Angie Tribeca’ Deserves ‘Something Bigger Than an Emmy’ in Hilarious FYC Video

In “Angie Tribeca,” the lucky guest stars often get more to do than parody a cliched suspect-type or teary-eyed victim. Chris Pine, for instance, plays a Hannibal Lecter-like villain in Season 3 who’s been imprisoned for years but can offer needed assistance to Angie Tribeca on a new case. Introduced in a bright blue jumpsuit standing stoically behind the glass wall of his prison cell, Pine pairs a faint British accent with a snake-like lisp to create Dr. Thomas Hornbine’s voice, both channeling Anthony Hopkins’ iconic performance in “The Silence of the Lambs” and lending a gaiety absent from Hopkins’ cold-blooded doctor.

It’s a subtle shift in tone needed to make the scene work and one constantly required to keep “Angie Tribeca” humming along. These scenes have to be played straight for the silly punchlines — like the Mennen Speedstick Maximum Security Prison’s tagline, “We keep sweat locked up.” — to land. Identifying this tone is half the battle for actors like Pine who are just popping in for a brief stint, and walking the line while joyously celebrating the madness of his character makes the performance an instant classic (even after so many others have parodied Hopkins’ Hannibal over the years).

Only a few episodes later, Portman is handed a different, if similar, challenge. The outspoken women’s rights activist is given the role of Mrs. Kraft, a NASA scientist who looks and acts like a ’60s housewife. The fact that she’s not given a first name is as intentional as her assumption that Angie works for Detective Tanner (DJ Cole) simply because he’s a man. Her constant smile, perfect makeup, and bursting baby belly all lend Mrs. Kraft an air of domesticity and her period appropriate surroundings further enforce the patriarchal era of NASA’s heyday.

Knowing how she really feels, one can only imagine Portman would be eager to satirize the sexist trappings of our past by emphasizing their modern parallels. But her line delivery is in keeping with Mrs. Kraft’s reality, not the social commentary her character offers to the audience. When Mrs. Kraft refuses to give a freshly baked cookie to Angie, offering her “a Fresca and a diet pill” instead, Portman whispers the line as if Mrs. Kraft would be embarrassed for Angie that she even thought to take a delicious treat meant for the hard-working men around her.

Now, Portman — an Oscar winner and three-time nominee — is obviously a pro, so complimenting her on understanding the basic concepts of acting may seem reductive. But the distinction she makes here isn’t that she’s playing a character rather than herself; it’s that her character isn’t in on the joke, unlike so many other satiric roles that require their performers to play up the meta connections made by the audience. Portman grasps the tone quickly and then runs away with the scene, her soft inflections and glowing expressions creating a beam of light gliding through the scene. Again, there’s so much more to the scene than celebrity worship, and that’s a credit to the writing as much as the performers.

Portman, Pine, and the slew of other celebrity guests who pop up in the first five episodes of Season 3 — including Michaela Watkins with the best pop-in line of the year during Episode 3 — help keep “Angie Tribeca” among the best comedies out there. They’re all deeply aware that the spoof only works when you take it seriously. They’re all LeBron James, and they all do so much without ever touching the ball.

Grade: A-

“Angie Tribeca” Season 3 premieres Monday, April 10 at 10:30 p.m. on TBS.

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