Temperature-programmed desorption (TPD) with ammonia is widely used for zeolite characterization revealing information on acidity and adsorption sites. The interpretation of TPD measurements is, however, often challenging. One example is the NH3-TPD profile from Cu-chabazite (Cu-CHA) which generally is deconvoluted in three peaks with contributions from NH3 on Lewis acid sites, copper sites and Brønsted acid sites. Here, we use density functional theory calculations combined with kinetic simulations to analyze this case. We find a large number of possible species, giving rise to overlapping features in the NH3-TPD. The experimental low-temperature peak (below 200,^circ text {C}) is assigned to NH3 desorption from Lewis acid sites together with NH3 desorption from a [text {Cu(II)(OH)}(text {NH}_3)_3]^+ complex. The intermediate-temperature peak (250{-}350,^circ text {C}) is attributed to decomposition of a linear [text {Cu(I)}(text {NH}_3)_2]^+ complex and a residual from [text {Cu(II)(OH)}(text {NH}_3)_3]^+. The high-temperature peak is predicted to have contributions from Brønsted acid sites (text {NH}_4^+), [text {Cu(I)}text {NH}_3]^+ and [text {Cu(II)}(text {NH}_3)_4]^{2+}. The present work shows that NH3-TPD from Cu-CHA can be reconciled with copper complexes as NH3 storage sites.