P.Herc. 1020, transmitting an Early Stoic text (probably by Chrysippus), was unrolled between 1803 and 1804 and is preserved in 13 pieces, which have come to us in poor condition. One piece has been proven not to belong to this papyrus on palaeographical grounds. The stratification of the pieces ranges from absent to severe. The original order of fragments was upset after some pieces were hung on the walls of the Officina dei papiri around 1865 and subsequently taken down at the beginning of the 20th century. It has been reconstructed both by measuring the 'voluta' of each piece and on the basis of Hayter's numeration either legible on the 'cartoncino' on which some pieces are fixed or inferable from the 'disegni'. The impossibility of identifying with certainty the text layout of the outer pieces of the roll because of the presence of multiple layers in them make it difficult to estimate with precision the length of the lost portions between them. In addition, the lengthwise compression of the papyrus roll permits only an approximation of its original length and total number of columns. As far as the preserved text is concerned, in addition to the 8 columns previously edited by Hans von Arnim, 18 inedited columns have been read and transcribed so far. A new critical edition of the book is currently being prepared within the framework of the project ERC Starting Grant 241184-PHerc (European Commission, FP7, 'Ideas')