★★★★ ½

Mildred Hayes is a woman on a mission. Seven months ago, her teenage daughter Angela was raped and murdered, but no arrests have been made. Mildred believes the local sheriff and his deputies aren’t doing enough to capture the killer. “They’re too busy torturing black folks to solve actual crimes,” she says. When she notices three dilapidated billboards outside of her hometown of Ebbing, MO, she rents them and puts up the following message: “Raped while dying.” “Still no arrests?” “How come, Chief Willoughby?” Needless to say, Willoughby (Woody Harrelson) doesn’t take too kindly to the billboards; neither do many of Ebbing’s citizens, who would prefer that Mildred grieve in private and not remind them of the horrible, unsolved crime. But Mildred won’t be silenced. She believes there’s a better chance of finding Angela’s murderer if she keeps the case in the public eye, regardless of the consequences.

Mildred is played by Frances McDormand in a fierce, no-holds-barred performance that ranks with the Oscar winner’s very best. Mildred is a deeply flawed, profane character (she curses out anyone who opposes her, and isn’t averse to ruthless acts of violence if pushed too far), yet McDormand manages to make her incredibly sympathetic and even likable. (Credit also writer/director Martin McDonagh’s unflinching, penetrating, and often hilarious script -- yes, Three Billboards is frequently laugh-out-loud funny.) While McDonagh (In Bruges, Seven Psychopaths) forces viewers to feel Mildred’s deep, inconsolable pain and witness raw acts of outrageous cruelty, he leavens the story with moments of tenderness, too. Even when Mildred is acting appallingly or delivering unfiltered, scathing dialogue, the result is so brutally honest that we cheer her on rather than turn away.

The film’s other outlandish character is Deputy Dixon (Sam Rockwell), a racist, dumb-as-dirt, and almost always slightly inebriated officer who thinks any problem can be solved with a few whacks from his billy club. Dixon is a bit too stereotypical of a redneck, and honestly, not all that believable as a character, but Rockwell is so good and so mesmerizing that we dare not look away and long for his return whenever he’s offscreen. It helps that McDonagh burrows beneath each character’s rather gruff exterior and exposes his or her individual (and mostly tormented) background and heartaches. These are all people who see their pursuit of happiness rapidly ebbing away, and come to realize they only have each other to rely on.

The movie’s supporting cast -- which includes Lucas Hedges as Mildred’s conflicted son, Caleb Landry Jones as the awkward owner of the billboards, John Hawkes as Mildred’s menacing ex-husband, and Peter Dinklage as a local pool-hall junkie -- are all excellent. The soundtrack is a dream too, with “Walk Away Renee,” “The Night They Drove Old Dixie Down,” and “Buckskin Stallion Blues” all perfectly placed.

Three Billboards, though filled with verbal and physical violence, is ultimately a film about understanding, forgiveness, and grace, even in the face of justice denied. It’s also one of the best movies of the year and should get lots of love come Oscar season. If it doesn’t, that would truly be a crime.