Is bicyclo[1.1.0]butane chiral?
Bicyclo[1.1.0}butane is an achiral molecule.  



Any molecule containing a plane of symmetry must be achiral and bicylco[1.1.0]butane has 2 planes of symmetry.  One plane bisects the molecule and passes through the 2 tertiary carbons, the other plane bisects the molecule and contains the 2 secondary carbons.

Even replacing one of the secondary or tertiary hydrogens with a substituent does not make the molecule chiral.  Such a substitution will remove one plane of symmetry, but not the other one.



In the above bicylco[1.1.0]butane where we have substituted a chlorine for one of the tertiary hydrogens, the plane containing the 2 bridgehead carbons and the chlorine still remains.  However, if you replace one of the tertiary hydrogens and one of the secondary hydrogens, the resultant disubstituted-bicylco[1.1.0]butane will be chiral since both symmetry planes have been destroyed and no other plane or axis of symmetry exists.