In theory yes, In practice maybe not but also yes at the same time.
If you were to use VPN and a tor network you remove one of the security layers in the tor network. tor uses relays and your path changes every time you use tor by using a VPN you would be using the same end point (assuming you went TOR -> VPN)
If you went VPN -> TOR, You would encrypt all of your traffic to your start point (The VPN Out interface) and then the TOR network would take over, the issue here comes with the VPN service its self, they could very easily see you are using the TOR network, this would be your weak spot you want to be under the radar with everything.
To make it secure you would need to buy an anonymous VPN and pay for it in bitcoins after rolling your bitcoins via a tumbler (depending how you obtain the bit coins will determine your weak spot in the chain, but the tumbler should fix most of that issue). To also secure the purchase make bitcoin transactions and VPN transaction VIA TOR.
then once you have the anonymous VPN you would not want to connect to your VPN from your home address (though anonymous VPNS hold no data so technically you shouldn't be able to be traced from your home address). then once connected to the VPN you can use the TOR network that way.
Personally I wouldn't use proxy chains it would become pointless seeing as you are using TOR also proxy chains leave behind clues on your machine (they like to leave behind messages about how they connected to the proxy chains). also it really makes the process slow for very little benefit.
Using a VPN creates an issue with its self as to obtain the VPN you would use personal information. though any extra security would be nice as you mentioned the chain is only as strong as its weakest link. The VPN would be the weakest link with personal information following you back (using a free VPN would end up in records being kept of your activities).
Keeping data private is not the issue here, its keeping the data disassociated from the owner. 01/01/1970 is someones birthdate, asking someones birthday can be a security question...sadly I dont know who this birthday belongs to, following?
Hopefully I kept mainly to the point in my answer.