Is bicyclo[1.1.0]butane chiral? I think it isn't, but if one of the hydrogen atoms bound to the tertiary or secondary carbon atoms is replaced with e.g. chlorine, the formed compound will be chiral, right?
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.