We have carried out high contrast imaging of 70 young, nearby B and A stars to search for brown dwarf and planetary companions as part of the Gemini NICI Planet-Finding Campaign. Our survey represents the largest, deepest survey for planets around high-mass stars (≈1.5–2.5 M⊙) conducted to date and includes the planet hosts β Pic and Fomalhaut. Despite detecting two new brown dwarfs, our observations did not detect new planets around our target stars, and we present upper limits on the fraction of high-mass stars that can host giant planets that are consistent with our null result.