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$\require{mediawiki-texvc}$A stellar chromospheric activity database of solar-like stars is constructed based on the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Low-Resolution Spectroscopic Survey (LRS). The database contains spectral bandpass fluxes and indexes of Ca II H&K lines derived from 1,330,654 high-quality LRS spectra of solar-like stars. We measure the mean fluxes at line cores of the Ca II H&K lines using a 1 $Å$ rectangular bandpass as well as a 1.09 $Å$ full width at half maximum (FWHM) triangular bandpass, and the mean fluxes of two 20 $Å$ pseudo-continuum bands on the two sides of the lines. Three activity indexes, $S_{\rm rec}$ based on the 1 $Å$ rectangular bandpass, and $S_{\rm tri}$ and $S_L$ based on the 1.09 $Å$ FWHM triangular bandpass, are evaluated from the measured fluxes to quantitatively indicate the chromospheric activity level. The uncertainties of all the obtained parameters are estimated. We also produce spectrum diagrams of Ca II H&K lines for all the spectra in the database. The entity of the database is composed of a catalog of spectral sample and activity parameters, and a library of spectrum diagrams. Statistics reveal that the solar-like stars with high level of chromospheric activity ($S_{\rm rec}>0.6$) tend to appear in the parameter range of $T_{\rm eff}\text{ (effective temperature)}<5500\,{\rm K}$, $4.3<\log\,g\text{ (surface gravity)}<4.6$, and $-0.2<[{\rm Fe/H}]\text{ (metallicity)}<0.3$. This database with more than one million high-quality LAMOST LRS spectra of Ca II H&K lines and basal chromospheric activity parameters can be further used for investigating activity characteristics of solar-like stars and solar-stellar connection.