Source: Tafsir al-Ahlam al-Kabir (Ibn Sirin)
The chair in a dream is authority, high status, and power. Sitting on a chair indicates marriage for the unmarried, or travel, or gaining authority. Falling from it indicates dismissal from a position.
Source: Ta'tir al-Anam fi Ta'bir al-Manam (Al-Nabulsi)
The chair indicates a noble woman or a maidservant. For a pregnant woman, it is a baby boy. A chair of iron indicates a strong, powerful man.
Source: Al-Isharat fi Ilm al-Ibarat (Ibn Shahin)
The chair is interpreted as high status and a high position. Whoever sees himself sitting on a chair will gain a proxy or guardianship.