I would seriously second Anthony Shaffer's "Murderer" for it's breath-taking opening and seriously...fourth Ira Levin's "Veronica's Room". That one is an evil little chiller of a play.
There's another overlooked thriller from the '60's called "The Playroom" by Mary Can't-remember-her-last-name about a group of spoilled/misunderstood wealthy kids who fake a kidnapping. The original kids on Broadway included Karen Black, Richard Thomas and Christopher Norris.
You might want to try to find a copy of "Children,Children" a thriller in which Gwen Verdon made her non-musical stage debut about a baby-sitter getting psychologically terrorized by the children she is watching. It closed on opening night.
"A coherent existance after so many years of muddle" - Desiree' Armfelt, A Little Night Music
"Life keeps happening everyday, Say Yes" - 70, Girls, 70
"Life is what you do while you're waiting to die" - Zorba