$eta$ Car is a massive, eccentric binary with a rich observational history. We obtained the first high-cadence, high-precision light curves with the BRITE-Constellation nanosatellites over 6 months in 2016 and 6 months in 2017. The light curve is contaminated by several sources including the Homunculus nebula and neighboring stars, including the eclipsing binary CPD$-$59$^circ$2628. However, we found two coherent oscillations in the light curve. These may represent pulsations that are not yet understood but we postulate that they are related to tidally excited oscillations of $eta$ Cars primary star, and would be similar to those detected in lower-mass eccentric binaries. In particular, one frequency was previously detected by van Genderen et al. and Sterken et al. through the time period of 1974 to 1995 through timing measurements of photometric maxima. Thus, this frequency seems to have been detected for nearly four decades, indicating that it has been stable in frequency over this time span. These pulsations could help provide the first direct constraints on the fundamental parameters of the primary star if confirmed and refined with future observations.