In Spanish, the word for laugh is reir. Chabacano also uses this word, but with some alterations. The word is 'ri' (with a stress at the end). I am not sure if there is anyone who says 'rei', which is what someone who studies Chabacano and knows Spanish would guess the word for 'laugh' should be in Chabacano.
Some people would say 'ri que ri', which actually means to laugh a lot or to laugh and laugh. Throughout time, people started treating this phrase as one word and eventually came to mean simply, to laugh. Some people pronounce this as 'ri-ki-ri'. Others say tare or tari and think that it is a single word meaning to laugh. In reality, ta is a present tense marker and therefore this should be treated as two words, ta ri, or ta re.
The construction 'verb+que+verb' (meaning to do something again and again) possibly came from Philippine Spanish. From my limited knowledge of Spanish, I don't believe this expression exists in contemporary Spanish. This expression occurs a lot in Chabacano though. One will hear Chabacano speakers say 'come que come' (to eat a lot), etc.
Camins' Chabacano dictionary lists both ri and rei, while Santos' only has the word ri.
Here are some sentences using the Chabacano ri.
Chabacano: Por que tu ta ri?
English: Why are you laughing?
Chabacano: No tu ri, kay puede tambien aquel pasa contigo.
English: Don't laugh because that might happen to you also.
A very interesting expression in Chabacano that is connected to this word is 'mori de risas'. This simply means to laugh out loud or literally, to die of laughter.