Who said, "I am as empty as the space between the stars."

This is a fairly good approximation of the quotation, but isn't completely accurate. In Raymond Chandler's The Long Goodbye, the narrator says that he was "as hollow and empty as the spaces between the stars," which I assume is what you are referring to in your question.
The narrator of this novel is one of Raymond Chandler's most well-known and well-remembered characters, the dectective Philip Marlowe. Philip Marlowe was one of the originators of the hard-drinking, smooth-talking private eye archetype known to us now from many Hollywood movies of the 1930s and 1940s, appearing in multiple novels by Raymond Chandler—many of which were adapted later into films. Marlowe was most famously played by Humphrey Bogart.
When he makes this comment towards the end of The Long Goodbye, Marlowe is expressing the fact that he has "no feelings"—literally, he feels as if he has been hollowed out as a result of what has been uncovered and what has taken place over the course of the investigation. In this novel, several people are killed, many of them suffering from issues personal to Raymond Chander—specifically, characters struggle with alcoholism and insecurity. Raymond Chandler is understood to have projected something of his own personality into his detective character, Philip Marlowe, and autobiographical readings of the text have noted that Chandler's wife was, in fact, dying at the time he wrote this story. As Chandler struggled with the loss of his wife and with his own personal problems, something of this "hollow" feeling made its way into the story. The protagonist, Marlowe, is also feeling hollow because he has been betrayed—a man he became close to, Lennox, has turned out not to have been at all what he seemed, and therefore Marlowe is doubting his own capacity to perform his job adequately, as it has taken him so long to see through what Lennox is and what he has done. Marlowe has also borne witness to a number of tragic murders and suicides, the outcome of which is that, by the time he has gone through the subsequent inquests, he is feeling very drained, insecure and, as he says in this quotation, "empty."