Possible Water peak in PMMA nmr spectrum
Your peak at &delta;1.6 in $\ce{CDCl3}$ is indeed water. This is typical of the appearance of water in $\ce{CDCl3}$ at the sample concentration you present. Water can sometimes be broad; this depends on the overall sample concentration, acidity of the solution and relative concentration of other labile protons. This looks like a fairly new bottle of $\ce{CDCl3}$.

You will notice that the residual chloroform peak at &delta;7.26 has $\ce{^{13}C}$ satellites; intensity approximately 0.55% of the parent peak, with a splitting of ~210Hz (so about 105Hz either side of the parent $\ce{^{12}C}$ peak). You will then also see that the water peak, although of similar intensity, does not have any carbon satellites. You could also confirm this by adding a small amount of $\ce{D2O}$, and observing a change in chemical shift for this peak.