Laura Linney getting her own show on Showtime is equivalent to if HBO debuted a show starring Christian Bale. It’s the perfect place for one of the best actors in Hollywood. It’s practically destined to succeed.

Indeed the premiere episode of “The Big C,” Showtime’s newest comedy, shows just how much potential the program has, mostly based on an outstanding cast.

Of course “The Big C” is propped up by the Big C herself, Cathy (Linney) who has another Big C, cancer.

Linney is hilarious in the first episode, thanks to her natural wit and the strength of the writing. There are plenty of notable one-liners in the first episode alone, most memorably a conversation between Cathy and her husband Paul (Oliver Platt). Paul has recently moved out, and the two are having dinner, so Paul can plead his case to move back in. But Cathy, who realizes how much time she has left, is re-evaluating her lifestyle. She remembers that Paul’s distaste for onions is the main reason she has not had onions in awhile. “I want onions to be a major part of my life in the next year,” she says, as stoically as if she was speaking about her illness. It’s a dinner conversation that ends with Cathy telling the waitress that she’s just having desserts and liquor.

Just when someone might start to think Cathy is an unsympathetic character, the viewer meets Cathy’s son. Adam (Gabriel Basso) constantly torments Cathy with the most lurid pranks. We first meet him as he pretends he’s a home intruder, putting Cathy in a headlock and waving a gun at her. Later on in the episode, he fakes cutting his own finger off while helping to prepare dinner. Adam probably needs to add a third dimension to his character in future episodes.

Then there’s sassy Andrea, played by the actress who portrayed the title character in “Precious,” Gabourey Sidibe. Andrea, a student in Cathy’s summer school class, casually strolls into class late and does not worry too much about it, saying Cathy usually takes forever to get to her point anyway. Cathy is a bit cruel in her accosting of Andrea for this behavior, but it seems well-deserved with Andrea’s devil-may-care attitude.

But the main comedic force of the show is, ironically, a virtual no-name, at least in a show that already has Linney, Platt and Sidibe. John Benjamin Hickey as Sean, Cathy’s homeless, bleeding-heart brother, provides the most laughs in the premiere.

See, Sean has an odd way of life. He will only consume trash because he thinks the country wastes too much as it is. So, as a patron leaves the fast-food restaurant where Sean and Cathy are dining, Sean asks for the departing patron’s tray full of half-eaten scraps. He then takes a seat next to Cathy and commences to eat. Yes, it is disgusting, but it is charmingly quirky at the same time. The only way Cathy can get Sean to take some food, sealed in a tupperware container, is by saying it is leftovers and she was going to throw it out.

Sean’s life is a zany sitcom existence, one that, if analyzed for too long, might douse a bit of surrealism on a show that is decidedly supposed to be about real-life scenarios and feelings. Sean’s character does not exactly fit in with the rest of the bunch, but it’s in the same way that Steve Carell’s character did not exactly fit into “Little Miss Sunshine,” nor did even Juno fit into her own movie. It’s okay to have a bit of surrealism, especially if it comes from such a scene-stealing character.

And let’s not forget that it is absolutely fabulous that Phyllis Somerville from “Little Children” has regular work on this television show. Somerville plays Marlene, Cathy’s neighbor across the street. Marlene’s friends have died, her husband died and now she says she’s waiting to die. Essentially Marlene adds yet another pessimistic, morose character to an already pessimistic, morose show chock full of those type of characters. But the premiere episode shows that Cathy and Marlene’s relationship looks like it will develop past this.

“The Big C” seems like a show that is using cancer as a launching pad for a “Bucket List”-type existence for its protagonist. Except, instead of skydiving and racing like the mediocre “Bucket List” movie had, this seems more an existentialist, introspective look at Cathy as an individual. Perhaps it will not last very long, due to the obvious restraints of the narrative it’s set up for itself, but as long as it does last, expect the fire of “The Big C” to burn bright and turn in some of the best television on the best network in television. And expect Linney to add yet another strong female lead character to a network that already has three of them in Nancy Botwin of “Weeds,” Jackie of “Nurse Jackie” and Tara of “United States of Tara.”

“The Big C” premieres on Showtime Aug. 16 at 10:30 p.m. To view the premiere episode early, visit YouTube.com and search “The Big C.”