Should a woman refrain from laughing in public? Is it against chastity?
It is not forbidden for a woman to laugh in public, but it would not be appropriate in such cases when it is done deliberately.
Allah the Almighty commands:
“Tell the believing women to reduce some of their looks, and guard their private parts. Tell them not to uncover their beauty except what is naturally seen. Tell them to put their headscarves onto their chests and not display their beautiful parts except to their husbands, their fathers, their husbands’ fathers, their sons, their husbands’ sons, their brothers, their brothers’ sons, their sisters’ sons, their women, those in their possession, those male attendants that have no sexual desire to women, or children who are not yet aware of the private aspects of women. Tell them not to stamp their feet on the ground for their beautiful parts to be noticed. Believers! Return all together towards Allah, so that you may attain what you hope for.” (24:31)
There is a possibility that a woman may laugh in public in order to attract the attention of other men. In such a situation, this attitude would be no different than stamping her feet on the ground for her beautiful parts to be noticed. So it would be more appropriate for a Muslim woman to avoid such behavior even if she does not intend to attract intention.