Is there any limit for the data that can be inserted into a private DICOM Tag?

I am creating a Secondary Capture DICOM file which has many private tags. The contents of a file (which is of 69 Mb) is is read as binary and inserted into a private tag (0099,1016) and the VR is set to OB. The size of the DICOM file thus created is about 75 MB.

Once the file is saved successfully, I am sending the same to PACS (I am using DCM4CHEE as the PACS) using C_STORE. But PACS throws an internal error (status 0x0110) and C_STORE operation fails.

PACS ERROR Logs:

Received: 
C-STORE-RSP
(0x00000000,"0x000000CA") # Group 0000 Length
(0x00000002,"1.2.840.10008.5.1.4.1.1.7") # Affected SOP Class UID
(0x00000100,"0x8001") # Command Field
(0x00000120,"0x013D") # Message ID Being Responded To
(0x00000800,"0x0101") # Data Set Type
(0x00000900,"0x0110") # Status
**(0x00000902,"rPos:26014 (0099,1016) OB #69899172, value length [69899172] exc") # Error Comment**
(0x00001000,"1.2.840.113747.37041.480038180.780.2459492811.3") # Affected SOP Instance UID

Is this issue related to the DCM4CHEE or with the DICOM file? Is there any limit for the contents that can be inserted into a private DICOM tag?

The VR of OB can have value up to 4,294,967,295 which equals 2^32 – 1 and you are well within the range. Are you following the rules for encoding the private data elements as specified in PS 3.5 section 7.8? It requires you to reserve a block of Elements by used of Private Creator Data Elements (gggg,0010-00FF). In your case you need to add Private Creator Data Elements (0099, 0010) to reserve private elements (0099,1000-10FF).