Global climate change is expected to affect the ocean's biological productivity. The most comprehensive information available about the global distribution of contemporary ocean primary productivity is derived from satellite data. Large spatial patchiness and interannual to multidecadal variability in chlorophyll a concentration challenges efforts to distinguish a global, secular trend given satellite records which are limited in duration and continuity. The longest ocean color satellite record comes from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), which failed in December 2010. The Moderate Resolution Imaging Spectroradiometer (MODIS) ocean color sensors are beyond their originally planned operational lifetime. Successful retrieval of a quality signal from the current Visible Infrared Imager Radiometer Suite (VIIRS) instrument, or successful launch of the Ocean and Land Colour Instrument (OLCI) expected in 2014 will hopefully extend the ocean color time series and increase the potential for detecting trends in ocean productivity in the future. Alternatively, a potential discontinuity in the time series of ocean chlorophyll a, introduced by a change of instrument without overlap and opportunity for cross-calibration, would make trend detection even more challenging. In this paper, we demonstrate that there are a few regions with statistically significant trends over the ten years of SeaWiFS data, but at a global scale the trend is not large enough to be distinguished from noise. We quantify the degree to which red noise (autocorrelation) especially challenges trend detection in these observational time series. We further demonstrate how discontinuities in the time series at various points would affect our ability to detect trends in ocean chlorophyll a. We highlight the importance of maintaining continuous, climate-quality satellite data records for climate-change detection and attribution studies.