Strong amplification in integrated photonics is one of the most desired optical functionalities for computing, communications, sensing, and quantum information processing. Semiconductor gain and cubic nonlinearities, such as four-wave mixing and stimulated Raman and Brillouin scattering, have been among the most studied amplification mechanisms on chip. Alternatively, material platforms with strong quadratic nonlinearities promise numerous advantages with respect to gain and bandwidth, among which nanophotonic lithium niobate is one of the most promising candidates. Here, we combine quasi-phase matching with dispersion engineering in nanophotonic lithium niobate waveguides and achieve intense optical parametric amplification. We measure a broadband phase-sensitive on-chip amplification larger than 50 dB/cm in a 6-mm-long waveguide. We further confirm high gain operation in the degenerate and nondegenerate regimes by amplifying vacuum fluctuations to macroscopic levels, with on-chip gains exceeding 100 dB/cm over 600 nm of bandwidth around 2 µm. Our results unlock new possibilities for on-chip few-cycle nonlinear optics, mid-infrared photonics, and quantum photonics.