Since the introduction of bolometers more than a century ago, they have been used in various applications ranging from chemical sensors, consumer electronics, and security to particle physics and astronomy. However, faster bolometers with lower noise are of great interest from the fundamental point of view and to find new use-cases for this versatile concept. We demonstrate a nanobolometer that exhibits roughly an order of magnitude lower noise equivalent power, 20zW/root Hzp, than previously reported for any bolometer. Importantly, it is more than an order of magnitude faster than other low-noise bolometers, with a time constant of 30 mu s at 60zW/root Hzp. These results suggest a calorimetric energy resolution of 0.3 zJ = h x 0.4 THz with a time constant of 30 mu s. Further development of this nanobolometer may render it a promising candidate for future applications requiring extremely low noise and high speed such as those in quantum technology and terahertz photon counting.