Well, chords are groups of notes played together. The clarinet can only play one note at a time, no matter how quickly that note is played and changed. So, in short, clarinets can play zero chords but many, many notes. Further information on what a chord is: groups of three or more notes played together for a harmonic sound.
An example of a chord would be the notes C, E, and G played together. Clarinets can however, play arpeggios which are the notes of a chord played in succession instead of simultaneously.
It is impossible to play a chord on a clarinet. Clarinet is a woodwind instrument. A clarinet can play only one note at a time just like most woodwind instruments. Keep in mind that a chord is formed from multiple notes. Many clarinetists have to play musical notes at the same time to make a chord.
Arpeggio is a type of broken cord that can be played with a clarinet. Arpeggio is made up of many notes and it is not sung at the same time. The notes of arpeggio are played one after the order in ascending and descending order. In conclusion, it is not easy or almost impossible to make chords with a clarinet.