It’s hard to believe that Peter Gallagher’s performance was never rehearsed, that the actor appeared onstage to read author/actor Tim Crouch’s convoluted script without ever having seen it before. Gallagher had only words mounted on a clipboard and directions whispered in his ear by Crouch before and during each scene. It’s an interesting piece of stage wizardry called “An Oak Tree” that opened recently at the Odyssey Theatre in Los Angeles.

The premise is that Crouch is a hypnotist who has accidentally killed a young girl with his car. Gallagher is the bereaved father who volunteers to participate in the hypnotist’s act. And with that the hypnotist becomes the puppet-master, leading the grieving father through a bewildering tangle of emotions, illusions, and anxieties, but leaving him (and the audience) with more uncertainty than catharsis.

Gallagher does a masterful job, underplaying his role and delivering his lines thoughtfully and quietly as Crouch urges him on. For Gallagher, it is a one-time performance, as part of the unique concept of this production is to have a different unannounced and unrehearsed actor play the father’s role each night. (Apparently the father can be played by either a male or female actor, since Frances McDormand played the part one night in New York.)

Crouch first presented “An Oak Tree” at the Edinburgh Festival in 2005. Since then he has taken it around the world and performed it from Moscow to Melbourne more than 250 times — each time with a new actor.

The title, and the concept itself, comes from a piece of artwork by Michael Craig-Martin that was mounted at London’s Tate Modern museum in 1973. The “art” consisted of a glass of water, three-quarters full, that the artist insisted he had changed into an oak tree. In an accompanying text, in the form of a Q&A, the artist explains that he changed the water into the oak tree when he poured it into the glass. To which the questioner asks, “Does this happen every time you fill a glass with water?” And the artist responds, “No, of course not. Only when I intend to change it into an oak tree.”

Crouch’s play runs 75 minutes without intermission, but even in that short interval it sometimes drags a bit. Crouch stands in a corner or holds his head in his hand for long moments or whispers through a muted microphone into Gallagher’s headphone. And Gallagher acts mostly with his eyes — either looking puzzled, like a deer in headlights, or tearing up as he insists that a tree is his daughter.

There is also a rather gross and unnecessary sequence in which Crouch convinces Gallagher that he is naked and that he has pooped himself, made a terrible smell, and has defecation running down his legs. Not a pretty concept.

Crouch, who has been hailed as “one of the most exciting theatre artists working in the UK,” directs this production with the help of Karl James and a smith. Unconventional and unusual, yes. Entirely convincing, not so much.

“An Oak Tree” will continue at The Odyssey Theatre, 2055 South Sepulveda Blvd. in Los Angeles Wednesday through Saturday at 8 p.m. and Sunday at 2 p.m. through Feb. 14. Call (310) 477-2055 for reservations.

Cynthia Citron can be reached at ccitron@socal.rr.com.