Temporal solitons in driven microresonator, fiber-resonator, and bulk enhancement cavities enable attractive optical sources for spectroscopy, communications, and metrology. Here we present theoretical and experimental observations of a new class of temporal optical soliton characterized by pulses with large and positive chirp in normal dispersion resonators with strong spectral filtering. Numerical simulations reveal stable waveforms over a wide new range of parameters including highly chirped pulses at large drive powers. Chirped temporal solitons matching predictions are observed in experiments with normal dispersion fiber resonators strongly driven with nanosecond pulses. Scaling laws are developed and provide simple design guidelines for generating chirped temporal solitons in bulk- and micro-resonator, in addition to fiber-resonator platforms. The relationship between the chirped solutions and other stable waveforms in normal and anomalous dispersion resonators is examined. Chirped temporal solitons represent a promising new resource for frequency-comb and ultrashort-pulse generation.