BTH is negated. Because Chain Links are resolved backwards. Here is your problem
CL = Chain Link
CL1 - Monster Summon
CL2 - BTH
CL3 - RD
Resolves
CL3 - Trap cards cannot be activated
CL2 - Effect negated because of RD
CL1 - Monster summon is succesfull
Since RD and BTH are the same Spell Speed, they may be chained to one another.
IF your opponent had activated BTH AFTER you activated RD, then it wouldn't have been negated, because BTH would've resolved first. But then again it would've missed the timing if that happened.