The heart of the debate on the structure of English relative clauses (Bianchi 2002a, 2002b) centers on whether the surface head should have both an external and internal source (the Matching Analysis; Sauerland 1998; Hulsey and Sauerland 2006) or just an internal one (the Raising Analysis; Bhatt 2002; Bianchi 2000, and Kayne 1994). A recent analysis (Hulsey and Sauerland 2006, following Carlson 1977) argues that both structures are available to the grammar, and are typically licensed in distinct environments (1). If there are unique interpretations (LF representations) associated with the two structures, these interpretations should be dependent on the proper licensing of their respective structures (2). I present novel evidence supporting view (1), by showing that a semantic ambiguity for Concealed Questions, known as Heim’s ambiguity, in fact reflects the structural ambiguity of relative clauses. In particular, it is shown from several tests that while one reading (Reading A) is available whenever the Matching structure is licensed, another reading (Reading B) is available just in case the Raising structure is.