Chlorophyll content, as the primary pigment driving photosynthesis, is directly affected by many natural and anthropogenic disturbances and stressors. Accurate and timely estimation of canopy chlorophyll content (CCC) is essential for effective ecosystem monitoring to allow for successful management interventions to occur. Hyperspectral remote sensing offers the possibility to accurately estimate and map canopy chlorophyll content. In the past, research has predominantly focused on the use of hyperspectral data on canopy chlorophyll content retrieval of crops and grassland ecosystems. Therefore, in this study, a temperate mixed forest, the Bavarian Forest National Park in Germany, was chosen as the study site. We compared different statistical models (narrowband vegetation indices (VIs), partial least squares regression (PLSR) and random forest (RF)) in their accuracy to predict CCC using airborne hyperspectral data. The airborne hyperspectral imagery was acquired by the AisaFenix sensor (623 bands; 3.5 nm spectral resolution in the visible near-infrared (VNIR) region, and 12 nm spectral resolution in the shortwave infrared (SWIR) region; 3 m spatial resolution) on 6 July 2017. In situ leaf chlorophyll content and leaf area index measurements were sampled from the upper canopy of coniferous, mixed, and deciduous forest stands in July and August 2017. The study yielded the highest retrieval accuracies with PLSR (root mean square error (RMSE) = 0.25 g/m2, R2 = 0.66). It further indicated specific spectral regions within the visible (390–400 nm and 470–540 nm), red edge (680–780 nm), near-infrared (1050–1100 nm) and shortwave infrared regions (2000–2270 nm) that were important for CCC retrieval. The results showed that forest CCC can be mapped with relatively high accuracies using image spectroscopy.