How long till that pipe leaks? I am guessing not very long. Using drain cleaner increases the odds of problems like this showing up. The caustic vapors from the drain cleaner dissolve the pipe pretty quickly. Fortunately for a skilled plumber removing and replacing the corroded section of pipe can be done pretty quickly and easily enough.
While the plumber is fixing that corroded through pipe one may as well have the plumber fix what looks to be an amateur pipe joint off to the left.
Neglected piping systems within homes are a frequent cause of damages. Small leaks like these under sinks sometimes continue on for years causing water, rot and insect damages to the structure of the home that can be difficult and expensive to cure.
Take a look under the sink once in a while to see if any leaks or damages are occurring. It is much easier to fix a small plumbing leak than to replace the cabinet, floor structure and ceiling structures below.
I tell my clients do not ever use drain cleaner in a home you own. Nothing good comes from the use of drain cleaner.
In this case, corrective actions are necessary in order to avoid further damages from plumbing leaks.